I have spent the last half hour Googling this, and even enlisted Suburban Plankton’s help. We both came up with nothing.
We both remember a sketch or a brief part of a sketch in which a comedian (we remember him being black) is talking about young men wearing bandannas that are tied in front so that the knot is at their forehead. We remember him saying something along the lines of, “And what does that look say? ‘I’m bad; I’m a washerwomen!’?”
Does anyone else remember this?
I gave it a try too; the following got nothing remotely close on the major search engines:
"skit" bandana tied front
I do recall this, but I’m not hitting on this being a signature of any comic.
In spirit it sounds like Eddie Murphy but he likes to spit out the last word of a line and I think he wouldn’t have chosen the 4 syllable ‘washerwoman’.
I was thinking maybe Chris Rock, but searching for his stuff along with “washerwoman” got me nothing.
Maybe this will be one of those threads where 5 years from now someone comes back and answers. 
To me, “washerwoman” would indicate to me that it’s probably not a US skit. I don’t know if I’ve ever heard that term used in the vernacular in the US.