In Oklahoma ALL children not full time enrolled in school MUST have a scheduled nap time. They do not have to go to sleep but they must lay down and be quiet for at least part of it so that the children who nap can have no distractions.
Once they become full time school kids they are not required by the state to participate in nap time.
So if you were in Oklahoma she would still be required to lay down for the nap time. She would only have to lay quietly and not sleep if she didn't want to. Once the other children were asleep they would most likely let her have something quiet on the cot with her so she would be occupied for the 1 1/2-2 hours for nap time. Some will also have some activity the child can do at a table but they cannot disturb the children who are asleep.
The classroom is not to have lights on, the windows darkened, quiet music playing, no talking or moving stuff around. It is absolutely quiet time.
Again, once the other children are asleep the individual center will have their own policy about how they manage kids that don't sleep. Not required means they don't have to if the center chooses to allow them to get up and do quiet activities but it can also mean they can do quiet things on their cot like reading a book or doing a puzzle.
Here's the Oklahoma State licensing statement about nap time for non-sleepers. There is a LOT more said about the lighting and that it must be at least 80% dark in the room. Enough light to see their faces but dark otherwise.
http://www.okdhs.org/NR/rdonlyres/C###-###-####-C005-45D1...
This is from page 33:
"(d) Rest arrangements for preschool children.
(1) There is an individually assigned cot, bed, or mat with bedding for each preschool child who remains more than five consecutive hours in the child care center.
(2) Children who do not sleep have quiet activities available and are not required to remain on their cots or mats for an entire nap period.