The genus Natica is in the family Naticidae, commonly known as moon snails.
This genus is not native to Connecticut, except for a couple of small deep
water species which would not be likely sources of bead material.  Two
possibilities come to mind.  The beads you mentioned may have been made from
Polinices duplicatus, which is not a true Natica, but is a member of the
moon snail family, and is common in shallow water in Connecticut.  Or, the
beads or shells may have come from farther down the coast, around Florida,
where true Natica shells are available.
Paul M.
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