Ground crews at American Airlines are afraid to call in sick because the carrier allegedly retaliates against workers who do. That's according to New York City, which is suing American on behalf of 750 workers.

American assigned disciplinary points for every sick day used by employees, including agents, representatives, fleet-service workers and mechanics, the city's Department of Consumer and Worker Protection said in announcing the lawsuit. 

The carrier also failed to pay sick leave at the required rate, barred workers from using accrued sick time, and illegally required advance notice and medical documentation for short amounts of leave, the lawsuit filed claimed. 

"Workers in major transportation hubs where thousands of people pass through everyday should not have to choose between going into work sick or getting in trouble for exercising their right to take a sick day," Lorelei Salas, commissioner of the city agency, stated in announcing the suit, which seeks $375,000 in restitution. 

The airline denies the allegations. "American Airlines employees enjoy generous sick leave and benefits, including those set by union contracts with terms that are often more generous than required by the New York law," a spokesperson for the carrier told CBS MoneyWatch by email. "American will continue to work to make sure its team members have generous health and wellness benefits."

Under a city law that took effect in 2014, employers with five or more workers who work more than 80 hours a year must provide up to a week in paid annual sick leave. Those with fewer workers have to offer unpaid sick time. 

Around the U.S., a growing number of cities and states are mandating that employers provide paid sick time, a policy adopted by Walmart in February for its 1.1 million hourly workers. Pennsylvania's highest court last week rebuffed a challenge to a Pittsburgh ordinance requiring paid sick time for workers, letting the 2015 measure stand. 

Separately, thousands of American customer service agents recently signed a petition calling for the carrier to provide stools to give them a break from "countless hours standing in one place on their feet." The carrier did not return a request for comment on the appeal.