Me. Rev. Stat. tit. 21-A, § 341

A registered voter not enrolled in a political party may participate, subject to the restrictions of section 145, subsection 3, in a party's primary election without enrolling in that political party. An unenrolled voter may vote in only one party's primary election. The Secretary of State shall establish procedures to ensure that each voter voting in a party's primary election is offered a ballot for that primary election.