NEW YORK — For New York City, it wasn’t an unusual sight: a possibly mentally ill woman pacing and mumbling to herself on an elevated subway station platform.

The woman eventually took a seat on a bench Thursday night, witnesses later said. Then, without any warning or provocation, she sprang up and used both hands to shove a man into the path of an oncoming train.

As police sought on Friday to locate the unidentified woman, Mayor Michael Bloomberg urged residents to keep the second fatal subway shove in the city this month in perspective. The news of the horrific death of 46-year-old Sunando Sen, who was from India and lived in Queens, came as the mayor touted drops in the city’s annual homicide and shooting totals.

“It’s a very tragic case, but what we want to focus on today is the overall safety in New York,” Bloomberg told reporters following a police academy graduation.

The New York Police Department released a sketch of the woman and surveillance video of her fleeing the area and interviewed witnesses, including some who described her as acting agitated before the attack.

Some witnesses said Sen had been shielding himself from the cold by waiting in a stairwell before he ventured out onto the platform to see if the train was coming. They also said he had no interaction with the woman, who immediately darted down a stairway after she pushed him.

One witness told police that Sen had no time to try to save himself. The witness turned away to avoid seeing him getting crushed on the tracks.

Investigators identified Sen, who lived alone, through a smartphone and a prescription pill bottle he was carrying. They notified his relatives in India of his death.

Detectives were following leads from the public generated by the video and were checking homeless shelters and psychiatric units in a bid to identify the woman, described as Hispanic, heavyset, about 5-foot-5 and in her 20s. It was unclear whether the woman and Sen knew each other or whether the attack was simply the act of a deranged stranger.

The medical examiner said Friday that an autopsy found that Sen died from head trauma.

Commuters on Friday expressed concern over subway safety.

“It’s just a really sad commentary on the world and on human beings, period,” said Howard Roth, who takes the subway daily.

He said the deadly push reminded him, “the best thing is what they tell you — don’t stand near the edge, and keep your eyes open.”

Bloomberg, asked earlier Friday about the episode at a station on Queens Boulevard in the Sunnyside neighborhood, pointed to legal and policy changes that led to the release of many mentally ill people from psychiatric institutions from the 1960s through 1990s.

“The courts or the law have changed and said, no, you can’t do that unless they’re a danger to society; our laws protect you. That’s fair enough,” Bloomberg said on “The John Gambling Show with Mayor Mike” on WOR-AM.

There are no barriers separating the trains from the people on the city’s subway platforms, and many people fall or jump to their deaths in front of rushing trains each year.

Though shoving deaths are rare, Thursday night’s killing came just weeks after a man was pushed in front of a train in Times Square. A homeless man was charged with murder and is awaiting trial.

Other high-profile cases include the 1999 fatal shoving of Kendra Webdale, an aspiring screenwriter, by a former psychiatric patient. That case led to a state law allowing for more supervision of mentally ill people living outside institutions.

Like many subway riders, Micah Siegel follows her own set of safety precautions during her daily commute: Stand against a wall or pillar to keep someone from coming up behind you, and watch out when navigating a crowded or narrow platform to avoid being knocked — even accidentally — onto the tracks.

“I do try to be aware of what’s around me and who’s around me, especially as a young woman,” Siegel, a 21-year-old college student, said as she waited at Pennsylvania Station on Friday.

So does Roth, who’s 60.

“It sounds a little wimpy if you’re like, ‘Who’s going to push me?”’ he said. “But it’s better to be safe than sorry.”