G is for Gumshoe (1990) written by Sue Grafton

Three things happen to Kinsey Millhone on her thirty-third birthday: she moves into her remodelled apartment, which has finally been finished; she is hired by Irene Gersh, a sickly Santa Theresa resident, to head out to the Slabs in the Mojave Desert and locate her mother; she gets the news that Tyrone Patty, a particularly dangerous criminal she helped the Carson City Police Department track down a few years back, has hired a hitman to kill her.