If related to precipitation your house must have a moisture leak that
must be located and repaired.
In order of ease of inspection:
Check if the furnace flue is hot and DRY, a too large flue for the
current furnace can get condensation inside it.
Then, the furnace's heat exchanger, especially if it's and old furnace,
ought to be checked for stress cracks - these allow combustion fumes to
enter the ducts - and your lungs. Use a flashlight and small mirror for
a look inside.
You need to inspect all, and not less than all, the ducts, including the
return, for water infiltration and disconnected joints.