Greevey is a homicide detective working in Manhattan's 27th Detective Squad. He began his career in the 1960s, partnered with Don Cragen. By the beginning of the series, he is promoted to sergeant and partnered with Mike Logan, with Cragen as their captain. He is very close to Logan, even while having authority over him, and provides his younger partner advice and someone in whom to confide. Greevey is happily married to his wife Marie, with whom he has three children. A conservativeIrish Catholic, he sometimes looks down upon people, even murder victims, whose lifestyles conflict with his beliefs. For example, his opposition to abortion makes him uncomfortable investigating the bombing of a family planning clinic, which causes some friction with Logan, who is pro-choice. However, he seems at least tolerant of adultery, noting that while he himself has never cheated on his wife, "I don't judge. You can never know someone else's story". Greevey also harbors an open distrust of doctors, which began after a doctor incorrectly diagnosed him with an inoperable brain tumor. After seeking a second opinion, he learned that it was actually a subdural hematoma, and recovered shortly thereafter. Greevey carries a Smith & Wesson Model 36 revolver as his duty weapon. He draws it several times during the series, but never fires it. Greevey's partner prior to Logan was killed in the line of duty during a traffic stop.
Departure
Dzundza was disappointed when he realized that Law & Order would be more of an ensemble show rather than a show starring him. Though the cast liked his portrayal of Greevey, they increasingly felt uncomfortable around Dzundza, who was also under stress from the constant commute between New York City and his home in Los Angeles. Dzundza quit after the first season of the show, making his last full appearance in the season finale, "The Blue Wall". In the opening scene of the second season premiere, "Confession", Greevey is shot and killed by a hit man working for a crime syndicate he is investigating. He is succeeded by Sgt. Phil Cerreta. Greevey is the first detective within the Law & Order franchise to have been killed in the line of duty. Along with Nina Cassady, he is the second shortest serving detective in the series after Nick Falco.
Connection to ''Law & Order: Special Victims Unit''
Greevey is mentioned in a 2001 episode of the spinoff series . Prior to his death, Greevey and Cragen had worked on a case involving the murder of a college student named Jennifer Talmadge, and the disappearance of her infant son, Stephen. He took the case very seriously, working on it on his off time. After Greevey's death, Cragen took the case over and kept in touch with her parents. In the episode, Cragen, by now the head of the sex crimes unit, finds Stephen Talmadge while investigating a corrupt adoption agency. Cragen and his detectives later determine that the wife of Stephen's biological father killed Jennifer Talmadge and gave Stephen to the adoption agency. In the end, Stephen's biological father wins custody of him.