Some states allow you to just exchange information and then each party files their own accident report with the police and the DOT within an allowed amount of time, so long as the cars are only minimally damaged and nobody is hurt. If one party wants the police there, it is standard to wait. If both decide it not necessary, it is fine to leave. Either way, leaving or staying does not give rise to the avoidance of a finding of fault against one party or another. The state of Wisconsin is a Tort State (as opposed to a no-fault state). These are insurance related issues as opposed to legal issues, but utterly intertwined. The accident reports filed by each party, any police reports and other relevant data will be submitted to the DMV and the insurance, and the insurance companies will assign fault if the DMV or police haven't, either by agreement or inter-company arbitration.
Relating to your question, however, you will see the processes required HERE. In part, it states the following:
REPORTING AN ACCIDENT TO THE WISCONSIN DOT In some situations, you must report an accident to the Wisconsin Police. If the police
were unable to file an accident report, you must complete and submit a
Driver Accident Report within 10 days of an accident, if any of the
- The accident caused injury or death.
- Property damage to at least one person's property amounted to $1,000 or more.
- Damage to government property, other than vehicles, amounted to $200 or more.
If you fail to report an accident to the Wisconsin DOT, you may have
your license suspended. In the event that another driver offers to pay
for damages and asks you not to report an accident, you are still
required to file the report in any of the situations outlined above.
Your report must include detailed and current information regarding
your insurance coverage. The DOT will cross-check this information
with the insurance company shown on the report. If you did not have
liability insurance when the accident occurred and were unable to
provide restitution for injuries or damages sustained due to your
negligence, your driving privileges will be suspended. You will be
required to file proof of future financial responsibility (SR-22) in
order to have your driving privileges reinstated.
Make a copy of the accident report form for your personal records. You
can mail the original directly to:
Traffic Accident Section, Wisconsin Department Of Transportation,
Po Box 7919,
Madison, WI 53707-7919
As you can see, from your interpretation/description, you were not technically required to deal with the police, but you were required to exchange information, assess and give aid to the extent possible to the other driver, and so if the other called for emergency intervention it may be the other driver disagreed w/ one of these assessments (damage or injury).**
If you did exchange information, took photos, etc., you are probably ok. If not, certainly that will be problematic.
**I know you are saying there was no damage or injury. However, while you are saying this is what the other driver acquiesced to, it may be that it is not the case either afterward or he/she wanted to avoid (potentially dangerous) interaction at the scene. That said, while you can clearly see the situations by which the police are necessitated, you also indicate the other driver called the police. In that case, you probably should have stayed once you were alerted to that fact, as leaving puts you in the precarious position of only the other driver's side being documented by the police, and your absence may lead the officer to find you at fault or with something to hide.
The officer will file a report, either way, of which you must get a copy. If he disagrees with your assessment of the damage/injury and feels you left in the face of those situations proscribed, you will know because you will be arrested or summoned for leaving the scene. That is to be determined by the reporting officer.
In the future, if there is an accident and one driver explicitly states the police have been called, you should wait. You don't have to say anything at all to the officer, if you don't want to. In most states, all you need to do is give the officer your driver's license, vehicle registration, and proof of insurance. It always looks worse to leave the scene knowing they are coming, since it may lead to a determination that it was illegal to do so. Whereas, no additional harm can come from remaining present.
So far, I cannot find a state statute there whereby it is explicitly illegal to leave once one driver calls for emergency assistance. If I find this I will amend my answer and cite it.