A 3 year old should nap but only if they really need a nap.
Some 3 year olds need a nap to refresh them and some 3 years olds do not need a nap.
It's all up to the individual 3 year old on whether they need a nap or not.
My first kid needed a nap until he turned 4 years old and my other kid stopped taking naps at 2 and 1/2 years of age.
If your 3 year old seems like he or she needs a nap then have them take a nap but sometimes they may not need or want the nap.
If the 3 year old is tired enough to need a nap they will eventually lay down just about anywhere to take their nap.
Don't force them to take a nap because not all 3 year olds need a nap but some do.