You did not state your age, which can be an issue when driving into another state that has different laws with regards to how old one can be to have a learner's permit, junior license, etc. That being said to the best of our knowledge you can drive alone in Connecticut with a junior license but not with a learner's permit.
According the NYS DMV if you have a learner permit, junior learner permit or junior license you may drive outside of New York State if allowable by the other state laws.
Connecticut's DMV notes that the state allows one to drive with an out of state learner's permit if they are at least 16 years old and adhere to the same restrictions as their home state placed on their permit. The person must also be under the instruction of person who has held a driver's license for at least 4 years.
We would advise you to check with the CT Department of Motor Vehicles to verify you can drive alone in Connecticut at your age and with your NYS junior license. You should also see if there are any other restrictions or conditions you will need to follow when operating a vehicle in their state.
We cover young drivers car insurance needs so get a quote for New York state auto insurance here with us.