It depends mostly on the policy of the school/parish/diocese. Generally speaking, most schools likely require participation at daily mass and prayer as Catholic school is Catholic. These schools are part of religious formation and classical education.
A Catholic, or any religious school for that matter, states that no one is required to participate in some aspect of the religious foundation of the school then they're not really a religious school.
Anyway, outside of daily mass and the like I'm fairly certain no other requirements are made, such as conversion, etc.