I got cert in Ohio, then I moved to Ok, I went to one of the nursing homes and applied and during the interview I explained to them that my cert is thru Ohio and that i needed to know how to go about transferring that. They pretty much took care of that, i think they called the CNA registry and verified that I did get my CNA thru Ohio and had the Cerrt transferred to Ok. i now work in Ar and they pretty much did the same thing here too. If you didnt' want to do it that way, you can call your states CNA registry or the State that you plan to move to and find out what you need to know.
It various from state-to-state. You have to find out if there is reciprocity between your current certification state and the one you want to move to. If there is not, you may have to start over.
You need to contact the state you want to move to and check. Usually, you can find info on CNAs under the State Department of Health.
There have been proposals, for years, to standardize the training across all the states so that certification would be transferable to every state, no questions asked. But that has not happened. Some of the states with more 'rigorous' CNA programs will not accept transfers (hence, no reciprocity) from states whose programs they feel don't meet their standards.