Short answer: sometimes. This is a little complicated, so bear with me:
When you look at the book in the library catalog, you'll see the call number listed. If next to the call number you see "(LIB USE ONLY)", that means the book is not allowed to leave the library, including overnight. If you do not see "LIB USE ONLY" there, it means that you can take it out overnight if you check it out less than two hours before closing; for instance, after 6:00 p.m. Mon.-Thurs. (See library hours.) It will be due one hour after the library opens the next morning.
For examples, take a look:
Some more details: We close at 5:00 on Fridays. This means that you can check a reserve book out after 3:00 on Friday, and it would be due at 10:00 am on Saturday (1 hour after we open.) We close at 3:00 on Saturdays and are closed on Sundays; so if you check it out after 1:00 on Saturday, it would be due at 8:30 am on Monday. And then there are holidays... When in doubt, ask a librarian!