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School districts may create a policy allowing students to be released for religious study, or they may choose not to coordinate with released-time programs and require the students' legal guardians facilitate the process.
Read more about "May" and "Shall" state laws

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13-33-10. Released time for religious instruction.

A child may, on application of his parent or guardian, be excused from school for one hour per week for the purpose of taking and receiving religious instruction conducted by some church or association of churches. The school board shall decide at what hour pupils may be excused. No such instruction may be given in whole or in part at public expense. The school board may allow the student to accumulate up to four hours of excused leave time to be taken consecutively on any one day or two hours to be taken on any two days.

All school districts, regardless of whether they are required by law to allow released time, should implement good policy and be prepared for when a released time program may approach the district. The time to set the policy is before an active program is pressuring the district. Research polices the district can implement to protect teachers' and students' instruction time. Set polices that limit disruptions to students and the ability for proselytization to occur, impacting other students of faith or no faith. A more detailed write-up on school board policies can be read here.