Stephen Suttie spoke the officer in an aisle in the Morrisons in Paisley, near Glasgow - just 10 days after he tried and failed to seduce another woman at the checkouts.
Suttie, 45, could now be jailed for up to a year for the offences, which took place less than two years after he was spared jail for stalking a librarian in the town.
Suttie, of Paisley, admitted his guilt over his latest crimes when he appeared in the dock at Paisley Sheriff Court this week.
Procurator Fiscal Depute Claire Rowan told the court he targeted the female police officer on May 22 this year - 10 days after he had tried and failed to charm another woman in the same supermarket.
The prosecutor explained: "[The female] Police Constable was on plain clothes duty and had attended Morrisons to purchase a refreshment.
"She dropped an item on the floor and bent down to pick it up.
"The accused approached her from behind, leaned in to her face.
"He said, 'hey, sexy, that's what happens when you're sexy - you drop your cold meat'.
"[The female] PC was alarmed by his conduct.
"She asked the accused who he was.
"He replied, 'sexy - I said when you're sexy you drop your cold meat'.
"She stood up and the accused appeared to notice her police badge, which was on a 'Police Scotland' lanyard, and stated, 'Police Scotland', is it? Still sexy'."
She then identified herself as a police officer and asked for his details, before summoning a colleague, who was elsewhere in the store, to help.
Some 10 days earlier, Suttie acted in a similar way towards another woman in the store.
Miss Rowan explained: "She looked over to the self-service checkouts.
"He looked over and, after making eye contact, held an intent stare and began to flex the muscles in one of his arms.
"He then licked his index finger and ran it up his torso from around his waist up to his chest."
She told a manager in the store but the matter was not reported to police until the incident with the female police officer.
Suttie admitted two charges of communicating sexually with the women against their will and was placed on the Sex Offenders' Register.
Sentencing was adjourned until next month for background reports to be prepared, including an assessment from professionals who work with sex offenders in Renfrewshire.
In July 2017, Suttie was spared jail at the same court over "an all-consuming infatuation" with a librarian.
He hounded the woman for a whole year, repeatedly turning up at her work, waiting for her to leave and then following her once she left.
He also repeatedly commented on her physical appearance and moved close to her any time she ventured out from behind her desk.
He became infatuated with May Gormley, who had worked at Paisley Central Library for 29 years at the time, after he started visiting the library most days in December 2015.
And, between June 1, 2016, and June 22 2017, he carried out a course of conduct towards Gormley which caused her fear and alarm.
He pleaded guilty to a stalking charge and was placed on a Community Payback Order for that offence.