In your case, it depends. In general, whenever you amend your Federal return, you should also amend your State return, unless you are not required to file one. You should most certainly amend your Resident state return - the Non-Resident return may not need to be filed or amended as most states do not require you to file if your income is under a certain amount.
Here's where to check out Virginia's Who Must File . Failing to file a required return will generally result in a notice from that state requesting you to file the amended return, but they are usually in no hurry to send them as the penalties for non-filing can be substantial.