Well not every state has enough state Senators such that twice that number would be a large enough even number that ties between parties would be very unlikely. Of course there's always the chance of independents holding the ballance of power, but imagine if the partisan balance in the Minnesota state House was 67 Democrats, 66 Republicans and 1 moderate Independent. The Democrats would have fully half the seats in the Legislature, so it's different than Independents holding the ballance of power and the situation the Republicans would be in, but would not have a majority. I'm not saying that it couldn't work, but it would be pretty odd. Has something like that ever happened in Minnesota, btw?
Hasn't yet, but it's not hard to see it happening. Republicans only have a 2 seat majority in the state House now, so the loss of one seat to an Independent or an incumbent leaving the party could create that.