The matrix clause is a normal clause; the RC is a CP modifier of the N, just like an AdjP (but following) or a PP.
"that" is a C (Complementizer) forming a CP along with it's complement: the regular sentence (within the RC).
And you should also have a trace (or other placeholder) where the relativized NP has been removed.
Roughly:
[TREE][NP [the] [dog] [CP [C that] [S t [smokes]]]][/TREE]
(Where 't' is a trace for the subject of the sentence that was moved to the C position as 'that'.)
Note: this is NOT specific to any particular approach (such as X-bar theory) but just a general outline. Apply details as needed.
