NEW YORK — Cookie Monster stands accused of shoving a 2-year-old. Super Mario was charged with groping a woman. And Elmo was booked for berating tourists with anti-Semitic slurs.

Times Square is crawling with entrepreneurs who dress up as pop-culture characters and try to make a few bucks posing for photos with visitors to the big city. But some of these characters are unlike anything you’ve seen on “Sesame Street” or at Disney World.

They smoke, they use foul language, and they can be aggressive. At least three of them have been arrested in the past seven months.

“He was using words that were really bad,” said Parmita Kurada of Stamford, Conn., who told police she got into a dispute this week with a man in a Cookie Monster costume who demanded $2 for posing with her son, Samay, 2.

Kurada said that when she told the Cookie Monster that her husband needed to get cash, the shaggy blue creature pushed the boy and began calling her and the child obscene names.

“It was very scary for us, and I was crying. I didn’t want to provoke him, so I said, ‘We’ll give you the money, but stop yelling!”’ she said.

Osvaldo Quiroz-Lopez, 33, was charged with assault and child endangerment.

In the wake of the arrest, the bustling “Crossroads of the World” was filled Tuesday with performers, including multiple versions of Mickey and Minnie Mouse, Hello Kitty, a Transformer robot, Lady Liberty, Super Mario and Elmo.

As street performers protected by the First Amendment, they are free to roam Times Square and work for tips that average between $2 and $5 a photo as long as they don’t block traffic, sell merchandise or demand payment, police say. That’s a ticketable offense that can cost about $60.

“I don’t think they should charge, but if they’re unemployed or homeless, and this is the only way they can make money, it’s OK,” said Lauren Larcara of Oakland, N.J., who posed with a torch-carrying Statue of Liberty.

Laura Vanegas, 45, changes into her Liberty robes and applies copper-green face paint behind the Times Square military recruiting station. She said she picks up $30 to $50 on her eight-hour shift.

Steve Crass, dressed as a robot in fluorescent red plastic panels, said he has made as much as $280 during his six-hour stint in front of Toys R Us. He acknowledged: “Some of the characters are a little too aggressive.”

Police spokesman Paul Browne said in an email that the department has had “occasional issues with the ‘faux paws’ in Times Square, but they’re nominal.”

The case against the Super Mario charged with groping is pending. The Elmo accused of an anti-Semitic rant pleaded guilty to disorderly conduct and was sentenced to two days of community service.

City Council Speaker Christine Quinn called the Cookie Monster case “just horrible” and said lawmakers have been looking into how to regulate the characters.

“It’s very challenging legally because dressing up in a costume and walking around Times Square is, we believe, a First Amendment-protected activity,” said Quinn.

Disney and the creators of “Sesame Street” did not respond to requests for comment.