I wouldn't mess around with just speaking to anyone in the police department. I would try and talk to the chief direct or someone near his level. City laws especially hunting supersede mostly anything county, state and especially the DNR. Each level won't know what the other is doing. If it's legal in Eagan to hunt, the chief or his counterpart will/should have detailed maps on where you can. As always, best to get something in writing as well. Never know when someone might call you in and you will have an encounter with someone who is on patrol at the time. Different people interpret laws differently.
Another option for hunting opportunities is becoming a member of the MBRB.
http://mbrb.org/mbrb/ Read up on the information on that link and if you have any questions, don't hesitate to call or email them. Now is the perfect time to get what you need settled for the MBRB hunts.
email -
info@mbrb.org (best method)
Phone: 651-895-7039