I think the original was in C major, but I’m not sure.
The tune starts on the 3rd and the first phrase ends on the tonic.
i.e. in the first phrase “When I get older, losing my hair”, “When” is on the 3rd (E in the original) and “Hair” is the tonic (C in the original). The tune contains accidentals that are not in the key signature.
If you want to play it with a backing track in concert C, the tenor notes will be in D and the alto notes will be in A. But you need to check whether you need to transpose up or down to fit comfortably within the range of the instrument,