Story highlights Governor's office says he'll meet with an LGBT advocacy group and the bill's sponsors

School restrooms and locker rooms would be limited to students of the same biological sex

Transgender students with written parental consent should be given a "reasonable accommodation," the bill says

(CNN) South Dakota could become the first state to ban transgender students from using restrooms of the gender they identify with.

The state Senate passed the bill Tuesday in a 20-15 vote , after the state House approved it 58-10 last month. The measure now goes to Republican Gov. Dennis Daugaard's desk.

If the governor signs off, school restrooms, locker rooms and shower facilities that could be occupied by multiple students may only be used by students of the same biological sex.

The bill states that if a student says he or she is transgender, and a parent "consents to that assertion in writing," the student should be given a "reasonable accommodation."

A "reasonable accommodation" could include a single-occupancy restroom, a unisex restroom or the controlled use of a restroom or locker room, the bill states.