Any type could have a passive aggressive response, but the manifestation of the response and the what would cause it will vary enormously according to type.
However since you asked which type is most likely to be passive aggressive let's see if we can narrow one down for you.
(What follows represents my opinion only).
As a general rule P's are slightly more likely to give a passive aggressive response than J's because J's extrovert their decision making and P's introvert theirs (hence if J gives an aggressive response it is more likely to be openly aggressive than passive aggressive).
Working back from that, I think it's fair to say that TP is more likely to have this response than FP. Both introvert their decision making but a TP, making decisions on logic or (what they see as) universal truths rather than the more instinctive feeling based process used by an FP. (FP's do not expect everyone else to share their feelings (since they don't communicate them) but TP's will expect people to share their logic because (to them) logic is a universal truth that should be held by all sane people). Therefore if the world goes against them a TP may display a stronger aggressive response.
Taking N or S into account, I'm thinking S here. A extroverted intuitive (as an NxP would be) might be better able to vent the aggression that way by throwing their ideas about a bit. An extroverted sensor would find this more difficult because extroverted sensing activities may not necessarily carry a suitable vent for the problem or issue.
As to E or I, probably I, thus putting the introverted thinking to the forefront and guaranteeing limited release form the auxiliary function of extroverted sensing.
That leads us to ISTP. If we look at the complete type dynamic we'll see, in order, Introverted Thinking, Extroverted Sensing, (Either) Intuition and Extroverted Feeling. Thus a passive aggressive response could be got from the dominant function, and hence is most likely. In grip (extreme stress), however, FJ properties will be displayed and the person is likely to become openly aggressive or emotional.