Interestingly the CP website says this:

"With its scenic views and hilly terrain, the Central Park Drives provide cyclists with a relaxing ride or a challenging workout, depending on their interest. No permit is required to bike in Central Park, however there are several laws and rules that every cyclist must obey: Pedestrians have the right of way at all times. At crosswalks, cyclists must slow down, yield to pedestrians and then proceed cautiously. Cycling is prohibited on all pedestrian paths except the marked shared paths at 96th St and W. 106th-108th St."