They can determine what isotope(s) are present to narrow the source.
Had a similar situation at a nuke plant I worked at like 30yrs ago. One worker was repeatedly alarming the exit rad portal monitor. Finally they got a team together to really investigate, including isotopic analysis. Turns out it was potassium-40. A forest fire somewhat nearby liberated naturally occurring isotopes, it settled in the nearby soil and then vegetation picked it up and sorta bio-concentrated it in young leaves. Deer ate the leaves and this guy ate a lot of venison. He brought some venison to the plant and it was mildly hot with that same isotope.