New York Consolidated Laws, Vehicle and Traffic Law - VAT § 1281. Traffic laws apply to persons operating electric scooters;  local laws

2. (a) Except as provided in paragraphs (b) and (c) of this subdivision, the governing body of any city, town or village may, by local law or ordinance, further regulate the time, place and manner of the operation of electric scooters, including, but not limited to, maximum speed, requiring the use of protective headgear, and the wearing of readily visible reflective clothing or material by operators of electric scooters, and may limit, prohibit the use thereof in specified areas, or prohibit entirely the use of electric scooters within such city, town, or village, provided that adequate signage is visibly posted outside the boundaries of such prohibited areas.

(b) The governing body of any city, town or village in the counties of Nassau or Suffolk may, by local law or ordinance, further regulate the time, place and manner of the operation of electric scooters, including, but not limited to, maximum speed, requiring the use of protective headgear, and the wearing of readily visible reflective clothing or material by operators of electric scooters only after adoption of a local law or ordinance by the governing body of the county in which the city, town or village is located.  Provided, however, that the provisions of this paragraph shall not apply to the adoption of a local law or ordinance by a city, town or village in the counties of Nassau or Suffolk pursuant to the provisions of paragraph (a) of this subdivision to prohibit the use of electric scooters in specified areas, or prohibit entirely the use of electric scooters within such city, town or village, provided that adequate signage is visibly posted outside the boundaries of such prohibited areas.

(c) The governing body of any town or village in the county of Westchester may, by local law or ordinance, further regulate the time, place and manner of the operation of electric scooters, including, but not limited to, maximum speed, requiring the use of protective headgear, and the wearing of readily visible reflective clothing or material by operators of electric scooters only after adoption of a local law or ordinance by the governing body of Westchester county.  Provided, however, that the provisions of this paragraph shall not apply to the adoption of a local law or ordinance by a town or village in the county of Westchester pursuant to the provisions of paragraph (a) of this subdivision to prohibit the use of electric scooters in specified areas, or prohibit entirely the use of electric scooters within such town or village, provided that adequate signage is visibly posted outside the boundaries of such prohibited areas.