Yes, they definitely do and can. Rabies spread by bats is a major concern for public health agencies all over the world. However it is important to remember that not all bats have rabies at the moment the research into this is a little limited but sampling shows us that in the USA only about 6% of bats have or have been exposed to rabies.
Most bats with rabies though are fairly easy to spot as it does normally make them very sick and these are normally easy to catch bats as healthy bats like to stay away from people. But the biggest problem with bats and rabies is that many bats seem to be able to carry rabies, get sick but then recover. So it can hard to determine if a bat that seems fairly healthy might still be able to infect people or other animals. For this reason anyone bitten by a bat (or any wild mammal) should wash the wound with soap and water (soap can actually kill the rabies virus so if there any on the skin surface or in the wound this should take care of it) and then see doctor. In areas were no rabies has ever been recorded it is usually fine but this is information local medical staff will have so that’s another reason to get it checked out. The bottom line is that you should always be careful when handling wild animals and this is especially true of any that look sick or seem too tame (animals with rabies often lose their fear of humans).