Our Fire and Police here in Roseville, CA use New World Aegis CAD and I believe it does allow export to various ESRI formats. I don't use it myself, though, so can't totally verify that it will do the export as you want.
Also, here's an article which seems to imply it has that capability:
New World upgrades public safety software -- GCN
Another:
New World Computer Aided Dispatch | Tyler Technologies
Chris Donohue, GISP