If you are moving your personal residence to another state, you are not required to move your corporation to the other state.  However, you will need some person or entity in the original state to serve as the registered agent of your corporation, basically to receive any legal papers relating to the corporation.

If you do decide to move your corporation to another state, you basically have two options.

Option 1. 

Leave your corporation in the original state of incorporation.  Obtain foreign entity operation status in the 2^nd state.  See article, Operating in Different States.

Option 2. 

Shut down the corporation in the original state of operation and open a new corporation in the 2^nd state (which then would become the new state of incorporation).

My preference would be Option 1.  This leads to continuity of the corporation.  In fact, if you are a 501c3, taking option 2 would mean you are a new corporation and must go back through the entire 501c3 approval process a second time.