The Green Party has two state legislators in Maine, Ralph Chapman and Henry John Bear. Bear doesn’t have the same power that most Maine legislators have, because he is a tribal representative, but Chapman is a full-fledged state house member.
The Maine legislature has adjourned but much business was not completed, and many legislators want to reconvene. Whether the legislature reconvenes depends on whether a majority of the three party caucuses wish to reconvene. So if the Democratic and Republican caucuses do not agree, Chapman can break the tie, because the Maine legislature recognizes the Green Party caucus. See this story.