My thoughts on the situation are the following: this is obviously a tough spot for the Patriots to be in. Had they known about the lawsuit and all of the other incidents surrounding Brown prior to Brown being released, they probably wouldn't have signed him. Due to the nature of his release and his all-pro talent, they didn't do enough due diligence when they signed him. It is what it is.
Now concerning the civil case, and the other incidents, it would set bad precedent for the Patriots to sit Brown or release him based on a civil complaint and rumor and innuendo. Mostly, it would be bad precedent for other players, and may make some players think that the Patriots "don't have their back."
From a PR standpoint, it would obviously be better for the Patriots to just sit him or cut bait.
The Patriots are now in an impossibly difficult situation. The best way to handle the situation in the long-term is to wait to see how the situation develops and how the league's investigation turns out.