Am I required by law to have a sign posted on my property where there are 2 units warning of unauthorized parking to tow

You must post a sign. Here are the requirements: Appropriate Signage - There is displayed, in plain view at all entrances to the property, a sign not less than 17 inches by 22 inches in size, with lettering not less than one inch in height, prohibiting public parking and indicating that vehicles will be removed at the owner's expense, and containing the telephone number of the local traffic law enforcement agency and the name and telephone number of each towing company that is a party to a written general towing authorization agreement with the owner or person in lawful possession of the property.

Yes, you need a sign. The law requires that there be a posting warning about towing before you can legally tow. Even if there weren't such a law, the tow company already told you they will not tow unless you have such a sign - you will not have much luck finding a legitimate tow company that will tow without the proper signage. Putting up the sign protects you and the tow company in the event that the car owner tries to sue you for illegal towing and protects the tow company's right to payment.

Yes you are required by law to post the sign and must do it or face statutory fines.