Officers across three New York City departments banded together to rescue a woman and her cat who were pulled out into the East River by rushing currents underneath the Brooklyn Bridge. NYPD officers were the first to respond to reports of a woman in distress — with her white cat in tow — in the river just before 3 p.m. last Thursday. A woman and her cat were dredged from the East River on April 30. NYPD The cops, alongside FDNY and New York City Department of Parks and Recreation officers, reached the shore near the end of the Brooklyn Bridge and lobbed a lifesaver into the brackish waters. The woman could be heard screaming and pleading for help as she clung to the preserver, body camera footage released by the NYPD shows. The cat was seen paddling further away from its owner. NYPD The responders tugged the woman back onto dry land using a rope hitched to the preserver. Halfway through the water rescue, one officer spotted a small, slow-moving speck in his peripheral. “The cat!…