I could not get the Connections plugin to work with Comprehensive Google Map plugin. So, I discovered a better (free) map plugin:
It is more robust, and perhaps more complex than I really need, but does play well with Connections.
Note: Prior versions of Connections, and cMap, worked fine with the Comprehensive Google Map plugin. You might try contacting the plugin developer, Alexander Zagniotov about offerng a way to turn off, Google Maps API v3..?