Your signature line shows Ct, and you are asking about a SC tag.
States generally accept the rules from other states on registrations, but a LEO will usually ask for your drivers license. If it is from one state, and the tag on the moped is from another, that line gets clouded.
If all your documentation is from the same source you will generally be ok. Exceptions to that will be on items considered safety issues, for example double towing in Ct will likely get you pulled no matter where the tag was issued.