401k and state taxes

I have yet another question. As a UK/US dual citizen domiciled in the UK how do I deal with
US state tax on distributions from a 401ks. These will obviously be taxed by the federal
government, but isn't state tax due as well? Should I treat the distributions as source
income in the state where I was last domiciled and submit a state return and then claim
a tax credit for the total of state and federal tax on my UK return?

This depends on the rules of each State(s) where you worked when ypu earned the money, whether or not you are still resident there for State tax purposes.

The UK answer is a whole bunch more complex again.  Such specific advice cannot be provided in an open forum.