Why did you say that Rama called the child? -Is this sentence ambiguous?- Does this sentence have the following two reading.
1. You said Rama called the child for some reason x, what is that reason X ( You said that Rama called the child for some reason, What is that reason? )
2. For some reason X you said Rama called the child , what is that reason.( You said Rama called the child, why did you say that?                                                                    Kindly give me an answer, Thanks in advance

Thank you Daniel, One more question See the following Sentence
1.  John  said that Raj  called the child to congratulate him for scoring high- what would be the corresponding " why question?" (  Why did John say Raj called the child ? - the embedded qn.reading)
2. John said that Raj called the child inorder to implicate that he too played a role in the incident of  assaulting the child. (   Im not sure whether I have expressed it clearly )

@binumal, the lack of a complementizer seems to help somewhat with the embedded readings, but they all seem weird to me regardless. As I said, my judgments are getting fuzzy looking at these too much.

@nico, that's the easy reading. What about the embedded one, asking about "why... [as you said] someone did something"?

Yeah, that's better than "why", although I still find it awkward.

I'm not particularly convinced by this particular trend of armchair linguistics to make claims based on judgments about these really weird sentences. I think there are semantic and pragmatic factors that should be investigated in real usage (e.g., corpora, probably too hard experimentally). Importantly, I don't trust the intuitions of anyone who has actually written about this because especially for something as subtle as this where my judgments are fuzzy after reading examples in passing, I just don't believe they can be reliable about it after spending perhaps years analyzing these sentences. There may also be dialectal or other factors to consider.

I'm not saying that the null complementizer analysis or that line of research is wrong. I'm just not convinced by it because the sentences seem very weird to me.

For example, one plausible alternative is just to talk about concreteness-- "why" is a very abstract thing that seems strange to talk about third-hand. But "what" is concrete and seems better. "When" is somewhere in the middle. My judgments basically correspond to that.

My guess is that in the right contexts all of these sentences would be uttered. But they all also come across as awkward to me, especially without (or in the wrong) context.

As for the lack of complementizer, I would also propose an analysis that points out a closer iconic bond between the clauses (without any interposed complementizer) would correspond more to the compression of the multi-layered question, making it more acceptable. This follows arguments by Givón and others for iconicity in terms of the tightness of syntactic packaging relating to the tightness of semantic relationships. See Givón 1991 on serial verb syntax for example, although I would emphasize that is only a tendency for SVCs and not a rule because it doesn't always work out cross-linguistically, as I'm finding in my dissertation research.

Givón, Talmy. “Some Substantive Issues Concerning Verb Serialization: Grammatical vs. Cognitive Packaging.” In Serial Verbs: Grammatical, Comparative and Cognitive Approaches, edited by Claire Lefebvre, 137–84. Amsterdam: John Benjamins, 1991.