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 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.