ยง  5-300.  Enrollment; generally. At the time a voter is registered or
  completes  an  application  for  registration  he  may  mark  his  party
  enrollment  within  the circle or box underneath or next to the party of
  his election on the application form.
Structure New York Laws
Article 5 - Registration and Enrollment of Voters
5-300 - Enrollment; Generally.
5-302 - Enrollment; Completion.
5-304 - Enrollment; Change of Enrollment or New Enrollment by Previously Registered Voters.
5-306 - Enrollment; Correction Of.
5-308 - Enrollment; Automatic Voter Registration.
5-310 - Enrollment; Forms of Affidavits, Mailing Requirements.