I doubt it. As I said, the Dominion was the side who declared war.
As I understand it, a legal
state of war doesn't exist, in this country, until declared by Congress--Germany declared war on us, but the Congress passed a bill of war on them (and Italy, and Romania, and so forth). Of course, there's no reason to believe that the Federation constitution even acknowledges legal states of war. It's not really necessary--you can't fight wars easily without needing them one bit.
I don't remember if the Dominion actually formally declared war on the Feds or anyone else.