New London, Connecticut, holds a mayoral election on November 5, 2019. The election is partisan. There are three candidates, including Green Party nominee Frida Berrigan. The New London League of Women Voters sponsored a mayoral debate and invited Berrigan, even though she is not on the ballot; instead she is a declared write-in candidate. See this story.
She had enough valid signatures, but some of the paperwork sent to the election authorities was lost in the postal mail, so she lost her spot on the ballot.
Exec/judic offices — NONPARTISAN Appv – pending Condorcet
When you only have three or four candidates running for a particular office, it does seem silly not to invite them all to participate in the debate.