No rule I'm aware of prevents this. Well, certainly none of the playing rules in the rule book. Maybe there's some obscure OHSAA rule I've never seen before. I do not now, nor will I ever, claim to be an expert on state administrative rules. That's something that, as an umpire, I don't need to deal with, so I don't bother learning them!
Rule or not, we are always taught to avoid anything that could even loosely be construed as showing favoritism toward one team of the other. For example, you should avoid assigning an umpire to work a game where a family member might be participating- even if the umpire is the most upstanding, nonbiased and honest person on the planet. Honest as he may be, if it presents even a whiff of a hint of a perception of possible favoritism, better to just find another neutral umpire.
Having the same umpire for every single home game presents more than a whiff of possible favoritism. I would think that you'd want to avoid that, even if there's no rule against it. You're just asking for somebody to take exception and complain.
