It's Alive III: Island of the Alive

A woman goes into labor in a cab on a rainy night. Panicked, the cab driver seeks out a police officer to assist in the birth before going to search for a public phone to call an ambulance. While he is away the woman gives birth to a mutant baby. Recognizing it as a mutant child, the officer tries to shoot and kill the infant, who reacts by killing the officer and mother. The following day the mutant baby's corpse is found inside of a Catholic church, where it dragged itself to die.