I agree with @NorthwestWA, it totally depends on which company you're working for, but I think to be on the safe side you must have worker comp insurance to protect you from any unforeseenIt really depends on the company you are working for. Some have it as a requirement no matter what. Others have it as a requirement unless your State RCW says you don't have to. Washington State for example does not require Workers Comp coverage if you are a owner/operator or an officer of the business. However your employees must have it. Some of our clients say OK no problem and others say "we don't care" you have to have it. Another client said OK you don't have to have it but we want to see that you have medical insurance so provide us with that info.
Basically start with the requirements of your client. Then if it is acceptable them you can comply with the RCW of your local jurisdiction.