Unless you're being admitted to a mental hospital for suicide watch etc then yes you can refuse to be admitted to the hospital.
A hospital will only admit you if you really need to be admitted so if you're being admitted to the hospital for care then that means that your health is serious enough to warrant a hospital stay.
So if you refuse to be admitted you could be putting your health at risk and risk getting even more sick and possible death if the health problem is severe enough.
When you go to the hospital and they say you should be admitted then you really should go ahead and let them admit you.
But if you refuse to be admitted to the hospital then you can do so but you must sign a form relieving the hospital and it's staff of any liability should you get even more sick and possibly die as a result.
So you can decide not to be admitted but you must sign documents to allow the staff of the hospital to release you from the hospital.