Yes, there are restrictions. You will need to check the US Customs requirements for the most recent reqirements. When we traveled from the US to Canada we had our 2 cats and a dog with us. We carried a folder with a current health certificate and a copy of proof of Rabies vaccination for each animal from our Vet. They didn't ask to see the information going into Canada; but they asked for it coming back into the US.
One thing I noticed when we crossed the border is that Canada required our cats to have the rabies vaccination to enter the country; whereas the US did not require the cats to have the rabies vaccination.
I would get the latest information so that you are up to date, just do an internet search for US Customs.
Marsha~