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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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15-806. Excuse from school attendance

A. The governing board of each school district and the governing body of each charter school shall adopt a policy governing the excuse of pupils for religious purposes. The policy may permit a pupil to be excused from school attendance for religious purposes, including participation in religious exercises or religious instruction. If the policy permits a pupil to be excused for religious purposes, the policy shall stipulate the conditions under which the excuse will be granted. These conditions shall include at least the following:

1. The person who has custody of the pupil has given written consent.
2. Any religious instruction or exercise takes place at a suitable place away from school property designated by the church or religious denomination or group.

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.