Applying for faculty position --wondering how long to expect to wait I applied for a faculty position. One month later  they asked  my references for reference letters.   I have not heard from them for a few weeks.  I have not been asked for a phone interview yet. Is it appropriate to touch base?
I am the chair of my department's faculty recruiting committee.  Yes, you should definitely feel free to contact the search chair to ask about the status of your application.

My department started accepting applications last October for faculty positions beginning in Fall 2016.  We automatically solicit reference letters for all assistant professor applicants, usually within a few days of the application.  We have invited almost all of our interview candidates at this point, but we may still invite more, and in principle, we can even continue accepting new applications.  Except for interview invitations, we normally do not contact applicants until the search formally closes, which will probably happen in mid-April.

It's probably safe to assume that if you haven't heard from a department (at least in the US) by now, they're probably not interested, but there are certainly exceptions.  My own job search is an example.  My current department invited me for an interview in late April, three weeks after sending me a rejection letter.  ("We changed our mind; we'd like to interview you.")  The framed rejection letter is hanging on the wall in my office.