Under the Republican bill, only candidates who trail the winner by 1 percentage point or less in statewide elections could seek a recount. Democrat Hillary Clinton lost to Republican Donald Trump by less than that margin in Wisconsin, but Stein -- not Clinton -- requested the recount.
Democrats have argued that if a candidate wants to pay for a recount, there's no reason to stop them.
The Senate passed the bill 20-13 Tuesday. The Assembly passed it in June. It goes next to Gov. Scott Walker, who supports the measure.