Long before Erika Menendez was accused of pushing a Queens man to his death on the subway tracks, her mother had called police at least five times over the past seven years to report erratic, sometimes violent behavior related to her daughter's mental health, a law-enforcement official said.

Over the past 12 years, New York City police have records of 14 encounters with Ms. Menendez, 31 years old, including nine arrests separate from the calls for help from her mother, the official said.

Two...