I basically agree with @Rick Wang here.
We have to assume a lot a this point, and that is never good. So here is a not good post LOL
From what I'm reading the tenant is in the Navi ("he's at see for the next 6 months") so active military (and everything going with it) can be assumed. It can, therefore, be assumed that it's not his duty weapon that was discharged as he was not there when it happened, assuming he's a good soldier following the rules of always leaving his duty weapon on base. If this is indeed the situation then this has nothing to do with his job and therefore I see no point in calling his CO or any other base personnel on this matter: none of their business and not helping the situation either. But that's j5mc on that particular part under those assumptions.
If the weapon wasn't even his then I do not see how this should be real grounds for eviction: Some person brought a weapon to his place and was dumb enough to handle it improperly (assuming that person didn't fire it on purpose which would never be proven anyway, though). While I would have a serious chat with my tenant making it absolutely clear that this is a big no-go (which I'm sure he knows already being a soldier) I would - taking everything else about his character etc into consideration - probably not evict him. Obviously, this can never happen again, and you may want to get this case documented in writing with him acknowledging the situation, your "reprimand", warning, and any further instructions, again in writing.
Should the police report, however, show facts that somehow "actively" involve him in this mishap (his gun, left out in the open etc) then I would probably decide differently, especially since, as a soldier, he has proper training on these things. It would therefore show clear neglect on his part and would mean there is likelihood for another incident of such sort.