CT knife laws?

i was wondering if there are any laws about the use or carrying of a japanese sword in Connecticut. Im a martial artist and i own a katana for martial arts practice. and since i was younger ive always assumed because i couldnt find anything about it, that i could not bring them off my property except for use in a dojo. so, i was wondering if there is anything that prevents or permits the taking of a japanese sword off ones own property. i know that in Japan one has to obtain a permit for such a weapon. but Im not sure how the laws pertain here.
 
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