Elisa Ball, 45, a first-term Democrat elected in November 2011, was treated at a Kingston hospital for injuries and released, she told the Kingston Daily Freeman, declining to say what the injuries were.
She also did not describe the vehicle that hit her and left the scene without stopping.
Kingston Police Chief Egidio Tinti told the Freeman his department had "an open investigation" into the Monday incident, which police did not initially report.
Tinto told the newspaper his department did not report the incident because it does not routinely publicize hit-and-runs. The department usually issues public notices only in the event of arrests or serious crimes, the newspaper said.
Ball is the wife of Kingston City Court Judge Lawrence E. Ball.
Kingston is a Hudson Valley city about 90 miles north of New York City.