question on background checks

I had an interview last week at a NYC area hospital. I was referred by someone on the inside so I did not interview with HR just directly with the hiring manager. Very pleasant person to interview any candidate regardless of the outcome. However she did ask me if I have any objections to doing a background check. I said no and she had me sign the document giving permission to run the check. She also asked how much notice would I need to give my current employers. In the end she told me human resources will contact me in about 4 wks. Is this a good sign? Second interview but the first never asked to run a check.