We are trying to identify metropolitan areas in the U.S. in which at least several government agencies are using both GIS and document managment systems.
Louisville, KY is one. Multiple local government agencies and departments use a shared GIS called LOJIC. Many of the same agencies and departments, plus others, are using a shared document management system called eB (now a product of Bentley). My own department also has a home-grown document management system. We are looking into migrating those documents to eB or a new system that meets our needs.
Not US, but Ludwigshafen in Germany.
We use a Webgis powered by ArcServer (IP-Syscon) which connects with "PitFM", da Document Management System. We connect our Documents with the Location and switch between the softwares.
I do not have specific example but I know Sacramento California is a full of government agencies using both.
Unfortunately not in the US so can't help there. But in Australia the local government City of Busselton connects their GIS with their document management system.
When they migrated their old document management system to link in with the GIS they found numerous lots that had not be rated (including beach front properties). So the ROI from doing this simple exercise was worth thousands of dollars a year on one property alone.