The couple had discussed the plot repeatedly in conversations the boyfriend recorded. According to court documents, Officer Cincinelli had also used social media to track the whereabouts of her boyfriend’s daughter.

Then on May 13, Officer Cincinelli met with her boyfriend to discuss the two hits, unaware that her boyfriend was wearing a wire. She offered a warped explanation of why the murders would not appear linked: They would take place on different days, and the attack at Mr. Carvalho’s workplace in Holtsville, N.Y., would not arouse suspicion “because the murder would take place in ‘the hood’ or ‘the ghetto,’” court records show.

The authorities went to great lengths to convince Officer Cincinelli that the plot had succeeded. Shortly after 10 a.m. on Friday, a Suffolk County detective contacted Officer Cincinelli at her home in Oceanside, N.Y., and told her they were investigating the death of Mr. Carvalho. Less than an hour later, F.B.I. agents sent her a text message, purportedly from the killer, along with a photograph of the supposed murder scene.

Immediately afterward, Officer Cincinelli contacted her boyfriend to align their alibis, and told him to delete their text conversations from his phone.

Later that day, she was taken into custody by the F.B.I. and charged with use of interstate commerce for murder for hire.

Officer Cincinelli joined the Police Department in 2007, according to police officials. She worked in the 106th Precinct in Queens as a domestic violence officer until 2017, when she was placed on modified duty and reassigned to a unit that monitors surveillance feeds in public housing developments. She was no longer permitted to carry a gun.

According to a detention memo, Officer Cincinelli had been disciplined by the department for sharing confidential information with a boyfriend. It is unclear if that boyfriend is the same source who informed the authorities of the murder plot.