What should I do with negative information I am uncovering about a criminal background?

First, you consult a friendly attorney, on the record, about the legal implications to yourself, of having the information, and about potential liabilities as regards libel. Perhaps from there a brief statement (not much longer than your sentence above) can be inserted referring to the material on file with that attorney or another responsible party.

If the matters are already part of the public record somewhere, you can add that location to your sentence as above.

As I have seen it in biographies, such a sentence can't help but be paired with an editorial comment as to how the matter might be viewed in light of their artistic contributions-- so-and-so had a few flaws vs. so-and-so's legacy was sadly [value statement] by [legal issue]... which goes back to libel liability, see?

Or allude briefly (your sentence above) to the existence of the issues and state that your work focuses strictly on their artistic contribution. Whatever you are finding can only be part of the story, in any event, so how would you know how to present it, absent quoting sources, and do you really want to spread that can or worms around THEIR reputations?

~Susan