(This arguably is a question for SE.Law, but because it's so aviation-specific I figured I would ask it here first)
A partner got this in a routine excise tax email from the Massachusetts Department of Revenue (MA-DOR):
Our records indicate that your Aircraft Registration in the Commonwealth of Massachusetts is set to expire on December 31, 2023.
If your Aircraft Registration has expired, as the aircraft owner, you cannot legally operate your aircraft until you receive your 2024 new registration certificate.
This got me a little curious. I could certainly see a state law which forbids locally registered aircraft from landing/taking off at state-owned airports, but I don't understand how one state can revoke airworthiness from the national airspace system. (I only have that excerpt to go off of, so don't know if a specific US or MA law was referenced. Thanks to @Chris, we have the relevant MA law: https://www.mass.gov/files/documents/2017/10/30/702cmr3.pdf)
Does a US state have US-wide airworthiness authority over airplanes registered within that state?
Update
I think this question is somewhat confusing because of a widespread mistaken understanding of what "airworthy" means. As MichaelHall shows in his answer, it's definition is "the aircraft conforms to its type design and is in a condition for safe operation." Unfortunately many of us, myself included, were taught that full paperwork compliance was also required for airworthiness. This led to me using the wrong word in the question.
I'm going to keep the original question as asked, because the answers are not wrong vis-a-vis the original wording. Fixing it would do a disservice to the existing answers, and if I need further clarification about state's ability to regulate aviation outside their borders I will ask at SE.Law.