I am 17 years old and I was playing with a play cap gun and an off duty police officer arrested me for deadly conducted . Is this possible?

Anyone can be charged with any crime. Whether the person is guilty of the crime depends on whether the conduct alleged actually occurred, and whether each element of the alleged crime took place. Police frequently arrest people for crimes that they only suspect have been committed, and the people arrested are often acquitted or have their charges reduced. You need to act promptly and take this seriously, even though the charges seem silly to you. A "terroristic threat" in Connecticut is a crime of threatening, not one of assault. The elements of this crime are described here: http://www.cga.ct.gov/2011/pub/chap952.htm#Sec53a-61aa.htm. This is a very serious matter. You need to be represented by an attorney. Let me know if you need a referral.