Section 37A. A voter desiring to vote by absentee ballot in a primary shall specify on his application for the ballot the party with which he is enrolled or, if he is unenrolled, the party in whose primary he desires to vote. A city or town clerk shall not supply any voter with the absentee ballot of more than one party at any one primary. If an enrolled voter requests the ballot of a party other than the party in which the voter is enrolled, the clerk shall supply the voter with the absentee ballot of the party in which such voter is enrolled.
The officers processing absentee ballots shall cause to be recorded upon the voting lists to be used at the polling place the political party in whose primary the absentee voter has cast his ballot if he is unenrolled, or the officers charged with the casting of such absentee ballot at the polling place shall so record on the voting list the political party in whose primary the absentee voter has cast his ballot if he is unenrolled.
If the voter was unenrolled before selecting a party ballot, he shall continue to be unenrolled and shall be recorded as unenrolled in the current annual register of voters.