I am conducting a short case study on grammatical gender in which two speakers - native German speaker and a native Russian speaker are given words in English and German. Both speakers are asked to determine the grammatical gender of the given words. My goal is to determine to what extent the native language influences speakers in their decisions when determining grammatical gender. For my case study I would need some scientific literature, i.e. other case studies, scientific papers which have handled the same or at least similar research questions.

Does anyone have any suggestions on scientific literature on grammatical gender?

Any help would be greatly appreciated! 

There has been a lot written about bilingualism and a lot about gender, as well as some (but less) about the interaction of the two. You'd need to provide more details about how you're approaching this: what do you expect the effects to be, and how will you measure them? I'm not sure I have specific recommendations for you, but so far this sounds like a big topic, rather than narrow enough to build a specialized bibliography for a literature review. I can't remember exactly where at the moment, but I'm pretty sure I've seen some studies comparing gender usage in different languages by bilinguals, as well as specifically, I think, studies on the challenges this poses during acquisition. It's vague to me how you plan to measure the cross-linguistic effects: is this a priming study? Are you looking for errors?

(I agree with the above, unless the bilingual methodology is meant to use English as a control to see lack of possible grammatical priming, but I'm not sure how the study will be set up, as in my question above, so I don't know whether that is relevant, or if English is probably not a good choice, as panini argued convincingly.)

Those words differ by natural gender (mother, father, etc.), but are not examples of grammatical gender (e.g. as shown via agreement) like in many other (European and other) languages. There is no grammar to test in English with those words, just lexical choices.
(The closest we get to grammatical gender would be the pronouns 'he' vs. 'she' and how they might need to match other words in a sentence, like 'his' or 'himself'.)

Yes. There's no grammatical gender in English.

That's referential, not grammatical, and only applies to animates. Sure, you can insist on that, in the same way that English has case-marking on pronouns, but no other nouns. Regardless, it is essentially irrelevant for any study of grammatical gender.

> A language only has grammatical gender if its nouns are divided into two
> or more classes which require other words to change their form to agree with them.
Yeah, this is a necessary condition. I wonder you or anybody could provide necessary and sufficient formulation -- A language only has grammatical gender iff (if and only if)… It is evident that your variant is not sufficient due to the following example: I/you/they work and he/she/machine/lion/lioness works. As far as I know, natives do not divide words by genders like this in English.
I would also like to take an opportunity to ask native English speakers what gender they use for the tin soldier and the paper ballerina from “Den standhaftige tinsoldat” and The Nutcracker from “Nußknacker und Mausekönig”? Thanks.

> That seems sufficient to me.
I use standard (scientific) logic and it does not in it. Necessary and sufficient/if and only if (iff) means binary equivalence (in strict terms). For example, a human is a male iff it has a penis. It means that if a human is a male it has a penis; and if a human has penis it is a male. An alternative definition might be “a human is a male iff it has the Y chromosome”. If this definitions mean the same than you may combine them as you wish for your purposes. Forbes has provided only if part of the statement because I have proven the reverse statement does not work (the terms are not equivalent). If they were it would be very convenient for the discussion and would solve a lot of problems. That is why people prefer the most strict definitions they can invent. Though iff-definitions are probably not always possible.

> As far as I can tell, that example is completely irrelevant: English does not have gender.
To claim this one needs:
1. A strict definition of what the grammatical gender is and everyone agrees with it.
2. A formal proof of the statement.
On the definition of the grammatical gender. Personally I believe the state of the art as following:
1. There is a simple strict definition I do not know.
2. There is an extremely overcomplicated definition like the formal grammatical case definition. I have already mentioned somewhere in this forum that such a definition of the grammatical case was firstly provided in a talk or two famous mathematicians and it required a very solid understanding of the algebraic group theory.
3. There is a definition that has not been found yet.
4. There is no a suitable unambiguous definition.

And for a formal proof of the statement it is sometimes much simpler to provide a counterexample that demonstrates the statement is not true. I believe I have done it with my counterexamples for a definition of the grammatical gender close to what Forbes has provided. These examples may be irrelevant if you do not agree with the definition (but I believe you should provide yours one in this very case). Personally I also believe that the grammatical gender is a kind of a feature that makes nearby words to change their form. But I do understand that such a definition is not enough, ambiguous, vague and so on. I do not know a better one.
> Generally any non-human "people" (especially characters in fiction) are referred
> to as "he" or "she" based on their assumed gender roles.
Thank you. It looks like the behavior is absolutely identical to the languages that no doubt have the grammatical gender. Personally I was not sure about this very case and “he is such a bitch” statement correctness in English.
> https://en.wikipedia.org/wiki/Thomas_the_Tank_Engine
Unbelievable. I have never heard about it but now I can guess that the Russian “The Little Steam-Engine from Romashkovo” is probably inspired by your Thomas.
> Generally "he", because of his voice and name.
Russian The Steam-Engine’s name is The Little Steam-Engine so he is male. Though his voice is the voice of an actress but it was made to make him sound as a teenager I believe.
The owl from the Winnie-the-pooh is female in Russian. It is female in the official translation, the cartoon and the most of the piratical translations. I do not know why it was not translated as the eagle owl (the most appropriate male word and it preserves all the characteristics and nuances of the personage) or the horned owl (a more morose male equivalent but still appropriate). Probably it was due to the first historical translation.
By the way, if I were a native English speaker Winnie would sound a little bit female for me. Though it is pretty male in Russian.
> I'm not really following the significance of this discussion at this point.
We have started to discuss the grammatical gender itself. The original poster just wanted to get a list of scientific literature on it. I believe he failed.
And your statements on the grammatical gender in English make feel it is not a science but a kind of a religion so far. But personally I find the discussion very useful because I have found that if a Russian boat floats in a river (female) then the boat floats in her; if the boat floats in a gulf (male) then the boat floats in him; if the boat floats in a lake (neutral) then the boat floats in him (I find it interesting); but if it floats in something neutral and vague (like in your dream) then the boat floats in it (very interesting). So, I will probably investigate the case (I mean I will address the professionals and see if they will be able to provide a satisfactory explanation for me).