Tenure Track application: Time for committee to respond after interviewing references
Yes, it's certainly fine to email them and ask.

However, I'm afraid you probably won't get good news.  A common workflow for tenure-track searches is that after one round of review, they only contact the candidates who were selected to move on to the next round.  It's likely that this has happened by now, so if you haven't heard from them, it probably means you're not one of the candidates they're actively considering. 

You technically haven't been rejected yet, because in principle, if the selected candidates don't work out, they could go back and reconsider the rest.  Indeed, official rejection letters often are not sent until after the search is complete and someone has been hired (or they've given up).  But this isn't a good sign.