All Hondas have a Powertrain Warranty upto 100K no matter you buy it from a dealer or private party. It covers your Transmission and Engine. Honda will replace the transmission if it fails under normal circumstances for free as long as all the scheduled maintanence was done on time and you have proof of everything. If you recently bought it, ask the previous owner for service records.
Usualy people take it to the dealer where they bought it from if they get any transmission problem, in your case you can call American Honda and get it done where ever they tell you to go.

Do all the maintanance on time and save the reciepts even for Oil changes and take care of the car overall and you will be ok.