install smoke/fire detector in basement
From the National Fire Protection Association:


  Smoke alarms installed in the basement should be installed on the
  ceiling at the bottom of the stairs leading to the next level.


I presume this is to detect smoke as it rises up the stairs. I have also read on the detector instruction sheet NOT to install smoke/monoxide detector closer than 15 feet from your furnace. I assume this is to reduce false alarms. If you have any doubts, you could certainly install more than one detector.

I have a similar layout in that I have a finished basement along with a separate utility room. I put a detector by the stairs as well as one in the utility room, about 10 feet from the furnace. No false alarms. Haven't had a fire to test this setup, thankfully.