You've Got Murder — Donna Andrews

Meet Turing Hopper. She's an Artificial Intelligence Personality--AIP for short--she's a mainframe computer with a mind like Miss Marple...and hardware that hides a suspiciously human heart.

AIP Turing Hopper is in a panic. Her creator, Zack, has missed work for several days. After exhausting her resources, Turing is still far from giving up. For, unlike other AlPs, Turing is sentient--and she senses foul play. Her skills of deduction may be virtually flawless. But it'll take more than that for a digital detective to catch a flesh-and-blood criminal...