NY- Should it be Starbucks or Star…bugs?

Current and former employees of the gourmet coffee chain filed a federal complaint yesterday claiming their corporate bosses have refused to heed repeated warnings about inadequate training and chronic infestations of roaches, rats and other vermin in New York stores.

But the company strongly denied the allegations, noting the complaints were coordinated by a handful of activists who are trying to unionize the chain’s normally merry band of baristas.

Out of the 201 Starbucks stores in the city, the Department of Health issued notices of violation to 44 for rodent or insect activity in the most recent round of inspections, city records show.

The complaints filed by Starbucks employees with the federal Occupational Safety and Health Administration focus on three stores – at Union Square East, E. Ninth St. and Second Ave., and E. 57th St. and Lexington Ave.

“I constantly have to deal with mice, cockroaches and fruit flies all over the place,” said Tomer Malchi, 24, who works at the Union Square store. “The root of the problem is that we’re never staffed properly to clean the place right and we never have the right equipment to clean the stores.”

Starbucks, which has refused to recognize the union, brushed off the allegations as “the latest tactic in an aggressive campaign against Starbucks and our partners that is designed to damage the credibility and good name of the company” by a “very small number” of current and former employees.

The average restaurant in the city received 12 violation points from the city health inspectors.

Among the 201 Starbucks stores in the city, 51 stores received 12 or more violation points.