Bettas don't 'sleep' in a sense. They do lie dormant and rest, if that what you mean. All fish do this. More or less. Sharks, for example, have to keep swimming to live, so they do it a different way.
But technically yes, they do rest or sleep. They don't stay active all day, thats for sure. My Ryu is so lazy... He likes to sleep in late!
*2 Bettas (for now RIP Ryu) *2 Goldfish *9 Guppies *1 Gourami *2 Chinchillas *2 Budgies *2 Dwarf Frogs *1 Dog *1 Cat *2 Hermit Crabs *2 3gs *1 10g *1 Pond *2 2gs