A hearsay declarant may be impeached under rules 608,609 and 613, among others. Often, defense counsel will seek to elicit a defendant's self-serving hearsay statement. Must I object and have an adverse ruling in order to impeach the defendant under one of these rules or may I allow the objectionable response and then impeach the defendant with testimony or extrinsic proof of convictions, opinion, reputation and/or prior inconsistent statements?

I think the rule to look at is 806. Several cases have approved attacking the credibiliy of a defendant after his unobjected-to hearsay was admitted through defense counsel.

Appling v. State, 904 S.W.2d 912, 916-17 (Tex.App.--Corpus Christi 1995, pet. ref'd) (State may attack credibility of appellant/declarant who invokes Fifth Amendment privilege not to testify);

Flores v. State, 2004 WL 1834399 at *1-2
(Tex.App.-Corpus Christi Aug 12, 2004, pet. ref'd) (not published)

Craig v. State, 2003 WL 21467209 at *1-2(Tex.App.-Houston [14 Dist.] Jun 26, 2003, no pet.) (not published)

One case to watch out for is Enriquez v. State, 56 S.W.3d 596, 600-01 (Tex.App.-Corpus Christi 2001, pet. ref'd) (where court of appeals divines that statement was not offered for its truth, declarant could not be impeached)

Ahhh...the beauty of the forum

We ran into the same situation in
State v. Jerry Lee Perez, unpublished 7th COA,
2/27/04

We did not object when the defendant's self-
serving hearsay statement was admitted. When
we tried to impeach w/ an inadmissable confession,
defense counsel and the judge wondered out loud
if we were laying behing the log. After
discussion of Appling, he let it in.

And in what good faith did the defense lawyer seek to elicit the defendant's hearsay statement? Oh,no, the defendant gets to ask for the hearsay and make the state object to look as though we are hiding the ball.
The more rational rule would be to acknowledge that the defendant wanted his hearsay statement in and he did so at the risk of the impeachment. There is "laying behind the log" and then there are sound tactics.