It began as just another bizarre scene in the Times Square area, a disoriented man lurching amid traffic, seemingly throwing himself into the path of oncoming cars.

The police arrived and the crowd grew. The hulking man continued on, ignoring the officers’ commands while eluding capture. Then the man reached into his pants pocket, withdrawing his hand as if it were a gun, the police said, and pretended to shoot at some of the officers.

Two officers opened fire, discharging a total of three bullets. They missed the man, but struck two women nearby, including one who had been leaning against her walker; the bullet wound to her leg sent her tumbling to the ground. Other officers rushed toward the suspect; a sergeant used a Taser on the man, and he was quickly subdued.

The shooting on Saturday night immediately raised questions about the police’s use of deadly force, especially in a crowded area where bystanders were in the line of fire. On Sunday, police officials, including the commissioner, Raymond W. Kelly, refused to say if the shooting appeared justified, saying that the circumstances were being investigated.