The state Senate passed the measure Thursday, sending it to Gov. Steve Beshear for his consideration. The bill previously passed the House.
House Speaker Pro Tem Larry Clark says his bill would be a way for state parks to raise more revenue.
Most state parks and golf courses are in counties where alcohol sales are prohibited.
The bill would allow residents of precincts where state park lodges or golf courses are situated to petition for the local-option elections. The ballot issue would be whether to allow alcohol to be sold by the drink at the local park or golf course.
The legislation is House Bill 475.