The Sleeping City (1950)

At Bellevue Hospital, New York, an intern is shot in the head by an unknown killer. Inspector Gordon of the 9th Precinct finds no obvious leads but senses an undercurrent of mystery at the hospital; enter Detective Fred Rowan, whose medical background enables him to pose as an intern. Through wheels within wheels, Rowan finally penetrates to a secret, dirty racket...and nurse Ann Sebastian, whom he's been dating, may be mixed up in it.