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.
Daugaard has said the measure sounds like a good idea but
plans to listen to recorded testimony before making a decision, the Argus Leader
On Wednesday, a spokeswoman for the governor said he hasn't taken a position yet.
"Before he makes a decision, he will be meeting with The Center For Equality
to understand their concerns," spokeswoman Kelsey Pritchard said. "He will also be meeting with the sponsors of the bill."
Earlier the governor's office had told the center -- which advocates for the lesbian, gay, bisexual and transgender community -- that he wouldn't have time to meet with them.
The governor has said that, to his knowledge, he has never met a transgender person.
Transgender student Thomas Lewis told CNN affiliate KSFY
the measure is unnecessary.
"Most of my male friends who I speak to a lot say, 'I don't mind if you use the bathroom with me,' he told KSFY. "I mean, it's a bathroom. ... It shouldn't be a big issue to begin with."
But State Rep. Fred Deutsch, who authored the bill, said the measure would help ensure privacy.
"The primary purpose of the bill is to protect the physical privacy of students from having to expose themselves, or be exposed to others, when in a state of undress or nakedness while at school or school functions," he wrote
The conservative Christian group Family Heritage Alliance Action praised the state Senate's approval of the bill.
"This is such the right thing to do to protect all of our students," spokesman Dale Bartscher told the Argus Leader. "It's a privacy bill, it's a modesty bill, it's sensible South Dakota common sense."
If the South Dakota bill becomes law, it would contrast starkly with legislation elsewhere in the country.
California's School Success and Opportunity Act, signed into law in 2013
, lets students participate in sex-segregated programs and activities, including sports teams, and use facilities consistent with their gender identity.