A Case of Need is a medical thriller originally published in 1968. I checked my copy out from the library.
Review:
Dr. John Berry, a pathologist, is interrupted at work by a call from his wife: Dr. Arthur Lee, an obstetrician friend of theirs, is in jail. John goes to see him and finds out what happened. Karen Randall, the daughter of a wealthy family, was brought into a hospital by her mother after an illegal abortion, bleeding profusely. She died, and Karen's mother claimed that Dr. Lee had done the abortion. Although he tells John that he did indeed speak to Karen, he hadn't performed the abortion - in fact, he'd turned her away, telling her that, at four months, she was too far along and he couldn't do it. She'd seemed to accept this and left, but clearly she'd gone to someone else instead.
Unfortunately, Dr. Lee makes a good scapegoat. He's half Chinese, so racism is a factor, and it won't take much work to uncover that he does, in fact, perform abortions (and people like John and other doctors helped him hide it). It won't matter to anyone but John and Dr. Lee's wife that he didn't perform this particular abortion. John figures that if he doesn't try to find out the truth, no one will.