Why was Jessica Rabbit's voice uncredited?

According to Bill Bryson's Made in America (p 295):

The longest credits yet - for Who Framed Roger Rabbit - lasted six and a half minutes and saluted 763 creative artists, technicians, and other contributors - without mentioning Kathleen Turner, the voice of Jessica Rabbit, who opted not to be credit.

Not sure why she would opt for this, but some thoughts:

1. Kathleen Turner recalls the film fondly in an interview with Nathan Rabin of Random Roles, which makes it seem unlikely that she had a problem with associating her name with the film.

2. The lack of credit may have more to do with the fact that she was 9 months pregnant while doing the voice for Jessica, her daughter being born on the last day of recording. It just may have not been something she was concerned about at the time.

3. Besides having a baby and building a house in 1987, between 1987 and 1988, she was in 4 films and a documentary. It is possible that there were contractual issues that kept her from being credited.

4. Because she was amazed by the creative achievements of others on the film, she may not have thought her contribution that noteworthy.

5. On a list of 763 names, who would notice?

Interview excerpt:

Who Framed Roger Rabbit (1988)—“Jessica Rabbit”

KT: Ooooh. Bob Zemeckis, what an extraordinary feat, matching animation and live film. Nobody had done that before. That was just a remarkable process. They kept sending me tapes of how it was going along, and how they were shooting a scene with Bob Hoskins and this sort of metal frame that was Jessica, that would be drawn over in later stages in the process. And then right up to when we had to start doing the breathing of the character, because it’s one thing to do lips and face, but the whole body is the breath, so [I had to] go in and do all the breathing so they could finish the body, and then go back to do the face. It was a fascinating process.

AVC: It was a technological breakthrough, but did you suspect she would become this widespread figure of lust?

KT: [Laughs.] I’m sort of amazed. Half the photos I get autograph requests for are Jessica. [Laughs.]

AVC: How much of you was in that character?

KT: Oh, to me, it was just fun. I was just seeing what I could do with that voice.

AVC: Do you see Jessica as another parody of the femme fatale?

KT: No. I believe she was sincerely in love with the rabbit. They had a good marriage.

AVC: There’s that famous line, “I’m not bad, I’m just drawn that way.”

KT: Well, yes, that was just too fun to pass up.

I don't know that you'll find an official answer to your question unless an insider can respond, but several facts may hint at some possibilities:

1. There were many rumors that came out concerning tension between disagreeing voices in the making of this movie (such as the notion that Mickey Mouse or Donald Duck couldn't appear without Bugs and Daffy appearing beside them, to avoid favoring Disney over Warner Bros.)

2. The movie was originally billed as a Disney/Spielberg collaboration, but ultimately released as a Touchstone/Spielberg collaboration.

3. Amy Irving, who was credited as you note, was married to Spielberg at the time.

In other words, you could come to the conclusion that there were a series of power plays between competing producers (and the director as a third factor), leading to behind-the-scenes negotiation that left Turner off the credits.

I did come across a reference suggesting that Turner and Irving both declined to be credited, as they wanted Jessica Rabbit to remain mysterious, but there was no source cited so there may be no truth to that suggestion.

It is worth noting that Turner was credited for Jessica Rabbit's voice for the subsequent animated shorts.