After the Attack on Sandy Hook Elementary School, Connecticut expanded it's list of banned weapons. It now includes .50 BMG variants, selective fire weapons, and certain semi-automatic "assault weapons". There is also a list of banned features on firearms. Any firearms fitting these categories, that were lawfully owned before April 4, 2013 have to be registered with the DESPP.
Some states have restrictions, banns, or require owners to register firearms they conceder to be "assault weapons". The definitions of an "assault weapon" varies widely from state to state. These definitions can include whether the gun is fully automatic, the magazine size it can carry, and others.