I think it would depend on how long you have worked at the other location. If it’s been a short time, I think it would be understandable to leave it out and then just discuss on a generalized basis with whomever you interview with. However, if you’ve been employed for a couple of years I’m not sure how it would look to leave it blanked out. Personally, I would add it but at any interviews I would make it known that I am CURRENTLY employed there and that it is NOT ok to contact that office at this time with any questions but that I would be happy to provide other professional references. An office should be respectful of that, I’d hope.
I recommend placing your current employment on your resume if its been a good length of time that you’ve been there. Most of the time they would be contacting your professional references rather than past or current employers. Just be honest when asking why you are leaving your current employment, most are understanding.