Passive-aggression is pretty much the antithesis to clarity and cooperation, creating unnecessary conflict and inefficiency. Your tolerance for it in the office thus should be slim to none. Still, there's more than one way to eradicate it, depending on the people involved and the specific circumstances.
Passive-aggressive people have trouble being direct about what they feel and think, which forces them to use more manipulative means of communicating. That said, while you might not have done anything wrong, it's important to remember that they are responding to you. Ask yourself if there are simple ways to modify your own behavior so the passive-aggressive individual can't "bounce" off what you're doing.
2. Ask for clarification.
Part of what makes passive-aggressive people keep on behaving poorly is that they think they're getting away with the manipulation. But they usually know that passive-aggression has negative connotations and don't want to be labeled as acting that way. Ask the individual if they realize they're coming off as passive-aggressive, or share what you've observed/heard and ask if there's something else they want to share with you. This lets them know they're not pulling the wool over your eyes and discourages them from continuing. At the same time, it provides an opportunity for a deeper discussion about their intent.
3. Help them out as a friend.
Being a buddy to a passive-aggressive person might be the last thing you feel like doing. But passive-aggression usually connects to some unmet need or stress. Think about what the individual is facing. Put yourself in their shoes and try to perform some acts of kindness that will build the trust that's necessary for them to tell you what's really going on.
4. Ask for their opinion.
Passive-aggressive people often resort to their behavior because they feel like they're not given the chance to express themselves any other way. If you ask them outright what they think, they'll feel more valued and will be more upfront with you. Get feedback often and take it genuinely to heart.
5. Ignore them.
While it's much better to get to build a relationship and get to the heart of why the individual feels like they can't be open with you, sometimes there are bigger fish to fry than making a huge deal out of what they're doing. Do the cost-benefit analysis, and if they won't stop even with other strategies, draw the line in the sand, leave their bait behind you and put your energy into what can move you forward.