If the other students generally get a vote in the selection process, then I would let the graduating ones do so as well. That's based on the presumption that all of the candidates have worked with the team long enough for the outgoing members to know how well-suited they would be for the jobs. If you don't normally let the non-graduating students elect the officers, then there's still a fair rationale for letting the graduates vote: they're presumably more experienced. (Or maybe you could base it on actual experience: a person gets one vote for each full FRC season, up to a maximum of four.)
While people often gravitate toward voting (and especially
first-past-the-post) as a way of making important decisions, it's worth considering whether that's really a good idea given your particular set of circumstances. Is every person supposed to have an equal say in the matter? Is it possible for the two best candidates to split the vote, and allow a third (who is supported by a minority only) to win? Is support from a plurality more important than the total amount of support a candidate receives?
To me, it sounds like the committee process, culminating in an
instant-runoff vote (rank the candidates) or
range vote (score the candidates) might give the voters some more flexibility in expressing their preferences.
Then again, it might be overkill if you're just choosing from a pool of three candidates, or something like that.
A lot of teams just let the mentors pick this stuff. That has advantages too—but depending on the internal politics of your team, that might not be wise.
And one more thing to consider: do you really want to put the candidates through an election process of any sort? Mightn't they have better things to worry about, than securing enough votes for an officership on a school team?