The police would still want an IP from you because they would then go to the ISP to ask which house that IP is registered to, or was registered to on the date the alleged offence took place if it’s a dynamic address.
Even the ISP can’t link it absolutely with an individual in most cases. I suspect that in most of the world an IP address is linked to an account holder but is used by everyone using the router for that account. So in my case the ISP would give my name, but my router is regularly used by at least 10 different people, some family members and some visiting friends.
Whilst an IP address wouldn’t necessarily link to a specific individual it can give the police a line of enquiry to follow. If the police want to use the information in a meaningful way then they would also need to provide a lot more evidence to conclusively prove that a certain person made a specific post on your forum.