Yes you can drop off the car in any state but there is an additional charge, not sure how much though.
Generally speaking, if you pick it up at an airport location and drop it off at another airport location in the metro NYC area there isn't an additional charge but be sure to check beforehand so you aren't surprised with an extra fee.
You can surely drop of at another Avis location in Connecticut but make sure either your contract states that or be ready to have a penalty being added to your rental. However dropping of at an Avis airport location might save some of those extra costs.
You can drop off anywhere but there will be a charger most of the time.
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