State Government website find an IP address?

I had someone use my email address and sign up on a State Government website and register as me. Made a complaint and the autoresponder of the .gov site replied to the email that I allegedly sent. When I saw it I replied that I did not send this and I did not live in this county. Can the State government website go into the registration and find that persons IP address who sent it? Thankfully this person did not threaten this person on their website. But who knows what they can and will do with it again. I am a Realtor and I have contacted Realtor.com and filed a complaint, as well as wrote the Senator back that I had not sent that email to him. I live in a different City and County in that same state.

My question is, can the state government find that person's IP address who registered as me? Thank you.