They can not "double dip" so to speak but resitution only covers certain things in the criminal case and additional damages may be sued for in civil case depending on what the exact case was about. If they are suing you you should hire a civil lawyer to assist you.
Attorney Chris Beck
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They can't double dip. If they are suing you for the same things as was awarded in the criminal restitution case, they can't sue you for that in the civil case. If there were things that weren't compensated in restitution, they are free to sue you for those as damages.
The information provided in this answer does not create an attorney-client relationship and is not considered to be legal advice.