The commercial energy code requires that a registered professional submit compliance documentation (construction documents and compliance verification). In the IECC, Section C103.1 Construction Documents, General, the wording states that construction documentation and other supporting data shall be submitted in one or more sets with each application for a permit. The construction documents shall be prepared by a registered design professional where required by the statutes of the jurisdiction in which the project is to be constructed. Where special conditions exist, the code official is authorized to require necessary construction documents to be prepared by a registered design professional.
The definition in the code for a registered design professional is: an individual who is registered or licensed to practice their respective design profession as defined by the statutory requirements of the professional registration laws of the state or jurisdiction in which the project is to be constructed.
As for COMcheck, there are no requirements as to who can use it and who can create a compliance report, but as to who signs and submits the report, the requirements stated above should be followed.