Its seems our surface ships do carry nuclear Tomahawks because the Japanese are complaining about it when our ships come to port.
I saw that, and found it a little puzzling. I'm thinking that this is Obama trying to take some political credit with his (in his words) "policy to pursue a world free of atomic weapons", but in reality I don't believe that there are any deployed. I'm pretty sure they're all in storage, and have been for some time.
The Navy has a standing policy of not confirming or denying what nuclear weapons are or are not on any specific ship, and it does cause some commotion from time to time. This happens constantly with our carriers.
I think the Japanese are complaining about the nuclear reactor that drives the ship, not the weapons the ship has.