I can't say for sure, but since its owned by the State of Delaware I would treat it like a State park.
Jonathan,I had asked this question a few months ago (incorrectly spelling Dickinson, so it wouldn't have come-up if you searched, sorry). That thread is here http://deccw.com/index.php?topic=4214.0I also never found a definitive answer to this question. For what it's worth, the State Division of Historic & Cultural Affairs website gives the history which includes: " In 1952, the National Society of the Colonial Dames of America in the State of Delaware purchased the mansion with 12 acres of land for $25,000. They presented the site to the State in Constitution Day ceremonies that year." See http://history.delaware.gov/museums/jdp/jdp_history.shtmlSo, I took that to mean it's state property, but never found any authority saying it was a "state building." Ultimately, I applied Sturm's logic and opted not to carry.