Is it possbile to start a criminal forgery case if parties live in different state??

Individuals do not prosecute criminal cases.  They are brought by the local prosecutor (usually a Distict Attorney acting on a citizen's complaint) and will probably have to be brought in the state in which the moving company operates.  Assuming that you suffered damages from the forgery, you can bring a civil case against the moving company in Virginia if the moving company has sufficient contacts with that state to allow the state to exercise jurisdiciton over it.  If the moving company moved  you to Va., you can probably sue in VA.  However, you should look at the contract you signed with the moving compalny to see if it has a mandatory arbitration provision or a provision specifying the court in which any litigation could be brought.