New York (CNN) -- The head of a group that promotes Times Square said Friday that he will lobby the new mayor to regulate dozens of costumed characters who inhabit the popular tourist destination after the arrest on sex abuse charges of a man dressed as Woody from "Toy Story."
A 44-year-old man was charged Thursday with three counts of forcible touching and three counts of third-degree sex abuse, said Detective Annette Markowski, a police spokeswoman. The victims were two females, ages 21 and 22.
The alleged abuse occurred around 8 p.m. Thursday at Broadway and West 46th Street in the glowing Times Square district popularly known as the crossroads of the world.
"This is the latest in a long series of disturbing incidents that reinforce our belief that these costume characters must be licensed and regulated," said Tim Tompkins, president of the Times Square Alliance, a nonprofit that promotes business development in the area. "We are looking forward to working with the new administration and City Council to come up with an equitable and effective regulatory solution."
Dozens of costumed cartoon characters and performers in Times Square have long solicited tips from tourists who have their pictures taken with them. City officials have struggled to regulate the characters without treading on their First Amendment rights. The characters and performers range from the Muppets to the scantily-clad, guitar-playing Naked Cowboy.
"Quirky is fine," Tompkins said. "Creepy is not."
Tompkins told CNN that his organization had recently been in touch with the administration of former Mayor Michael Bloomberg about taking steps to reign in the costumed characters but the ex-mayor's term ended before any action could be taken. He said he has made preliminary contact with office of Mayor Bill de Blasio about the issue.
De Blasio's office did not return calls seeking comment.
"The solution is to regulate and license these guys like any other business and then there's no first amendment issue," said Tompkins, referring to complaints that an all-out ban would violate freedom of expression.
A spokeswoman for Tompkins' organization said the characters and performers are "not officially endorsed by the intellectual property holders nor the Times Square Alliance."
Times Square, once a seedy neighborhood overrun with crime and porn theaters, has undergone a major facelift in recent decade, profiting from the draw of Broadway shows and its bright lights. A Times Square Alliance survey estimates that during high tourist summer months between 60 and 70 people gather around Times Square dressed in costumes or performing.
Thursday night's sex abuse arrest was the latest bad news involving the popular Times Square characters.
In April, a man dressed as the TV character Cookie Monster allegedly shoved a 2-year-old in Times Square after the child's parents refused the man's demand for $2 for posing for a photo, police said. The child was not physically injured. A 33-year-old man was arrested and charged with reckless endangerment and acting in a manner injurious to a minor.
In addition, the alliance said, a Spider Man character was arrested for punching a woman in February 2013, and a man dressed as Super Mario groped a woman in 2012. Both incidents occurred in Times Square.