The House had rejected Senate Bill 2911 on a 52-65 vote Monday.
It reconsidered the bill Wednesday, passing it 62-55. House Education Committee Chairman John Moore says he thinks some members were confused when they opposed the bill Monday, and he believes that confusion was cleared up by Wednesday.
Sixty-two school districts in Mississippi have elected superintendents, and 89 have appointed.
As the bill stands now, people in districts with appointed superintendents would vote on whether to continue the practice.
The bill returns to the Senate, which could either send it to the governor or seek final negotiations with the House.