Running the following returns a fair amount of information about what device a traffic group is on and its state. (edited for clarity)
get("/cm/traffic-group/stats")
...
u'https://localhost/mgmt/tm/cm/traffic-group/~Common~traffic-group-1:~Common~mybigip1/stats': { u'nestedStats': { u'entries': {
u'deviceName': { u'description': u'/Common/mybigip1'},
u'failoverState': { u'description': u'active'},
u'nextActive': { u'description': u'false'},
u'trafficGroup': { u'description': u'/Common/traffic-group-1'}},
u'kind': u'tm:cm:traffic-group:traffic-groupstats',
u'selfLink': u'https://localhost/mgmt/tm/cm/traffic-group/~Common~traffic-group-1:~Common~mybigip1/stats?ver=11.5.1'}},
u'https://localhost/mgmt/tm/cm/traffic-group/~Common~traffic-group-1:~Common~mybigip2/stats': { u'nestedStats': { u'entries': {
u'deviceName': { u'description': u'/Common/mybigip2'},
u'failoverState': { u'description': u'standby'},
u'nextActive': { u'description': u'true'},
u'trafficGroup': { u'description': u'/Common/traffic-group-1'}},
u'kind': u'tm:cm:traffic-group:traffic-groupstats',
u'selfLink': u'https://localhost/mgmt/tm/cm/traffic-group/~Common~traffic-group-1:~Common~mybigip2/stats?ver=11.5.1'}},