Several models of UPS's have both straight through (not on the battery backup) plugs and protected (on the battery backup) plugs. APC makes one (my wife's school uses them.) like that For example, the PC in her classroom at here desk is plugged into a protected socket, but the monitor and printer are on straight through sockets.
If you want to run the CM15A on a UPS, it should be on a straight through socket, not a protected (battery) one.