ยง  9-116.  Tallying ballots; generally. 1. As each vote for any office
  or position, or upon any ballot proposal, is announced, a clerk, or,  if
  there  be  no  clerks,  an  inspector,  under the scrutiny of a clerk or
  inspector of opposite political party immediately shall tally it in ink,
  with a downward stroke from right to left upon the official tally sheet.
  Each such clerk or inspector,  as  he  or  she  tallies  a  vote,  shall
  announce  clearly  the name of the person for whom he or she tallies it,
  or that he or she tallies the vote blank or void as the case may be, or,
  in the case of a ballot proposal, that he or she tallies the vote  "yes"
  or "no". When the name of a person voted for is not printed on the tally
  sheet,  such  clerks or inspectors shall write it in full thereon in ink
  in the place provided therefor.
2. When all the  votes  upon  the  same  office,  position  or  ballot
  proposal  shall  have been canvassed the tally thereof shall be verified
  by adding together all the votes tallied thereupon. Whenever  the  total
  number  of votes tallied (including blank and void votes) for any office
  or party position, divided by the number of persons to be  nominated  or
  elected  thereto,  or  tallied for any ballot proposal, does not exactly
  equal the number of ballots cast (including blank and void  ballots),  a
  recanvass must be made immediately in order to correct the error.
In  applying  this  section  to  a primary election the term "ballots"
  means the ballots of the party whose tallied  votes  for  an  office  or
  party  position  are  counted  as  above  provided. Upon a recanvass the
  clerks or inspectors must keep the tally  in  ink  from  left  to  right
  across the previous tally marks.
3.  When  the  errors  if  any  have  been  corrected  such  clerks or
  inspectors shall indicate the last tally opposite each name by forthwith
  drawing in ink a long horizontal line immediately after the  last  tally
  mark  opposite  such  name. Such tally sheets having thus been prepared,
  verified and closed, such clerks or inspectors shall sign their initials
  on each sheet, in any blank space thereof.
Structure New York Laws
Article 9 - Canvass of Results
Title 1 - Canvass at Polling Places
9-102 - Canvass; General Provisions For.
9-106 - Official Ballots; Accounting for Number Used.
9-108 - Canvass; Ballots, Verifying Number Cast.
9-110 - Canvass; Election Day Paper Ballots That Have Not Been Scanned; Method Of.
9-112 - Canvass Ballots; Validity of Ballot.
9-114 - Counting Ballots; Objections To.
9-116 - Tallying Ballots; Generally.
9-120 - Returns of Canvass; Generally.
9-122 - Proclamation of Result.