One, Two, Three Times A Murder - G. L. Barbour - Bog

Ben Nealy is a third-year medicine resident at New City Hospital in Cincinatti. Ben's life is not complicated until he becomes concerned that someone tried to kill a homeless man he treated in hospital. Senior staff physicians were unpersuaded, partly because the patient disappeared. Shortly, however, the patient showed up in the Emergency Department after a second episode that Ben believes is another attempt on the man's life. This time, Ben gets the attention of Tom Bolling, chief of staff at New City. Tom is a retired air force brigadier general and orthopedic surgeon with a long career of interest in quality-of-care issues, especially those beset by tradition. Tom thinks Ben may be right and asks his friend Detective Ron Looney to assist in the investigation. When Ron goes to get the man's fingerprints for identification and discovers the man has no fingerprints; the case seems to take a very dark turn at that point.
A combination of medical clues and police attention to detail develop a reasonable hypothesis after a third attempt of the man's life. Tom Bolling and his administrative staff manage an elaborate meeting with a suspect that allows Detective Looney to collect unusual data to solve the case.