DEFINITELY normal!!! LOL! I've had an adult dog do this as well. It happens when a dog is particularly relaxed and comfortable, especially if they are cozy warm. If it happens frequently, and the pup doesn't seem to grow out of it. I'd have the vet check him out. In that case it might be a UTI or some minor infection. This seems to be more of a problem for male dogs.
I don't think this is normal at all imo. Is the puppy desexed? sometimes if a pup is desexed early, especially in the case of females, there is a risk that they can end up incontinent. There is also a possibility that there may be a urinary tract infection. Best to have a urine test, I would think rather than delaying this and ending up with severe complications.