An Income Tax Replacing Property Tax

There was a woman I met while canvassing who had an interesting idea.

Institute an Income Tax, and anyone who owns property can send in a copy of their Income Tax payment and pay $0 for property taxes.

Would it work? Would property taxes stay at $0?

I don't want to see an Income Tax, but the bottom line isn't which tax is in place, but reducing the amount that people have to pay while making sure public services are still provided.