Make sure you read the 2nd page regarding rental activites.
If it's less than $650 they can be classified as a "Handyman" and, depending on the jurisdiction, would most likely have to have a business license for the county or city they were working in as well as liability insurance and workman's compensation. If not you would have to provide it.
In any event I would strongly recommend that you as the broker of record acquire a public liability and property damage policy for your brokerage. When law suits happen attorney's go for any/all deep pockets they can find.
Having been an expert witness in the construction defect arena for twenty years has made me very sensitive to the need for proper and adequate insurance. Hope this helps.
However, in general there only needs to be a broker of record in a property management company - as long as all you are doing is property management.
You should check with you E&O insurance agent to see if they might have additional requirements based upon the description of your business. Many of us do management and sales, so we have to either put up a huge wall between the operations or be more uniform in our license requirement.