Is it a requirement that I have a rejected Building Permit to submit an application to the ZBA?

No, but it is recommended, especially if you’re not sure if ZBA approval is required.  Even if you know you need to apply to the ZBA, it is still advisable that you seek an opinion from the Building Inspector.  This can help you identify the specific bylaw section(s) applicable to your petition to the ZBA.  It also helps identify all possible reasons for which a building permit might be denied.