I know this is from December, however, if you have not yet found out Jersey City only requires a CO for a number of specific reasons. If you purchased this 3-family and no changes have been made to the structure and if it's not new construction, you did not buy it from the City and you have not changed it's use then you should not require a CO. However, you should have received a Smoke Certificate at Closing, correct?
I hope you have already found your answer, but if not I hope this helps.
Have a GREAT day!
Emil Veltre, RPh, MS, CDPE