Here is how I screened my cleaner.  First off, I asked for references.  If they don't have any, I'd move on to the next option.  Secondly, I asked if she does background checks on each of her employees.  Third, I checked to see if they would provide me with a copy of their business liability insurance, which they happily provided.  If you ask these questions when selecting your new cleaner, you will have added peace of mind.