Are you saying the inspector left verbal notice with the owner that the work failed inspection, but gave no explaination why? This seems very unproffessional. As far as rules go: 80.19(F)(5) requires written notice stating the defects found. But article 80 may not have been adopted in your area. The applicable building code may have some applicable rules. IRC R109 requires notification of why the work failed inspection. This includes electrical inspections. The IBC has similar language, but doesn't seem to include electrical inspections. These code sections do not seem to specifically require a code section reference, but they do require a statement of the problem(s) found.
