The Collaborative International Dictionary of English v.0.48:

Roundsman \Rounds"man\, n.; pl. Roundsmen.
   A patrolman; also, a policeman who acts as an inspector over
   the rounds of the patrolmen.
   [1913 Webster]

WordNet (r) 3.0 (2006):

roundsman
    n 1: a workman employed to make rounds (to deliver goods or make
         inspections or so on)

Moby Thesaurus II by Grady Ward, 1.0:

69 Moby Thesaurus words for "roundsman":
   Argus, Charley, G-man, MP, airplane spotter, bailiff, beadle,
   beagle, bound bailiff, captain, catchpole, chief of police,
   commissioner, constable, deputy, deputy sheriff, detective, fed,
   federal, fire patrolman, fire warden, fireguard, flic,
   forward observer, gendarme, government man, inspector, lictor,
   lieutenant, lookout, lookout man, mace-bearer, marshal,
   mounted policeman, narc, night watchman, officer, patrol,
   patroller, patrolman, peace officer, picket, police captain,
   police commissioner, police constable, police inspector,
   police matron, police officer, police sergeant, policeman,
   policewoman, portreeve, reeve, scout, sentinel, sentry, sergeant,
   sergeant at arms, sheriff, spotter, superintendent, tipstaff,
   tipstaves, trooper, vedette, watch, watcher, watchkeeper,
   watchman