In recent weeks, spooked horses have knocked a 71-year-old man unconscious, overturned a car, and frightened theatergoers during a 15-block charge down Broadway.

The city keeps no statistics on the number of horse-related accidents, but there have been at least five incidents of horses losing their cool since January, and three since April 20. Just two incidents could be found for all of 2005.

In a city where ordinary people have been known to be driven out of their minds by the dense traffic and construction noise, some legislators are beginning to ask: What should be done after a 1,200-pound horse goes berserk?

After an accident in January, when a spooked horse put its driver in a coma and seriously injured two others in Midtown, Council Member Tony Avella, a Democrat of Queens, decided new restrictions were needed for the hansom cab industry.

“It is a very convoluted, very confusing legislation that allows the industry to exist now,” Mr. Avella said.

He said he is in the early part of his investigation, but he plans to hold a hearing on a bill to restrict the horsedrawn carriages to Central Park and to require more training for drivers.

Some veterinarians and animal advocates take a more radical stance, arguing that a crowded street is no place for horses at all. At about the time Mr. Avella was putting together his legislation,a group of animal advocacy groups formed the Coalition for New York City Animals to advocate for an all-out ban of commercial horses from the city.

In a letter to Mayor Bloomberg and the City Council, an equine veterinarian, Holly Cheever, said New York’s bad air conditions, hard surfaces, and dramatic summers make it an inhospitable and “inhumane” place for horse-drawn carriages. Spooking can happen to the best of horses, making it unsafe for both the horse and anyone nearby, she wrote.

The coalition’s campaign is currently restricted to hansom-cab horses, but it next plans to take on the New York Police Department, which has about 80 horses in its mounted unit and plans on adding more.

“It’s not a necessity to have mounted police,” the coalition’s spokeswoman, Edita Birnkrant, said.

Over the next three years, the Police Department plans to buy 75 horses, but they will likely replace many of the old ones, an NYPD spokesman, Jason Post, said.

Police said their horses undergo training that keeps them calm even when a firecracker is exploded at their feet or a gun is fired near their head. They are trained on different surfaces and in smoky conditions, Mr. Post said.

But even the police lose control of their horses, as was the case on April 20, when a saddleless horse galloped 15 blocks down Broadway, sending tourists scurrying. On February 20, a police horse slammed into two cars after it broke free of a mounted officer.

Drivers of the horse-drawn carriages aren’t taking the attacks on their profession lightly. At the start of the year, they formed the Horse and Carriage Association and hired a lobbyist to defend them against the proposed legislation.

“Overall, we have very few incidents,” the owner of a small carriage business, Joe, said. (He said he wouldn’t give his last name because of the pending legislation.) Referring to the proposal to restrict the carriages to Central Park, he pointed to the recent case of the bicyclist who was hit by an errant horse during training on the loop drive near 72nd Street.

“It would hurt the businesses financially, but it wouldn’t stop an accident,” he said.

At the end of the day, drivers still have to cross town to bring the horses to the stables, which are mostly along the Hudson on the Upper West Side, he said.

There are 68 licensed horse-drawn cabs and 374 licensed horse-drawn cab drivers in the city, according to the Department of Consumer Affairs. In order to receive a medallion, the horse must pass a medical test and drivers must complete a six-hour home study video course and pass a written and practical exam. The tests are administered by the Department of Health and Hygiene.

Many of the horses are bought from Amish horse breeders in Lancaster, Pa. Before bringing them to the city, carriage owners try them out in smaller towns in Pennsylvania.

Lawrence McKittrick, the avid 71-year-old bicyclist who was hit by the horse, said he doesn’t favor a full-out ban. He was knocked unconscious and had his hip dislocated when the errant horse charged him from the side. His injuries have prevented him from taking his daily rides since the incident on April 29.

“I am an advocate of maybe not using young, skittish horses,” he said with a laugh. “My hip is still pretty sore. My bike needs a little work, too.”