N.Y. VAT. LAW § 1123 : NY Code - Section 1123: When overtaking on the right is permitted

(a) The driver of a
  vehicle  may  overtake  and  pass upon the right of another vehicle only
  under the following conditions:
    1. When the vehicle overtaken is making or about to make a left turn;
    2. Upon a street or highway with unobstructed pavement not occupied by
  parked vehicles of sufficient width for two  or  more  lines  of  moving
  vehicles in each direction;
    3.  Upon  a  one-way  street,  or upon any roadway on which traffic is
  restricted to one direction of movement, where the roadway is free  from
  obstructions  and  of  sufficient  width for two or more lines of moving
  vehicles.
    (b) The driver of a vehicle may overtake and pass another vehicle upon
  the right only under conditions  permitting  such  movement  in  safety.
  Such  movement  shall  not  be  made  by  driving  off  the  pavement or
  main-traveled portion of the roadway, except  as  permitted  by  section
  eleven hundred thirty-one of this article.