OK I actually manage this person so it makes the situation more complicated.
This woman took over my job when I was on maternity leave. I wasn't too happy about her getting the job as she is a bit selfish in terms of allocating work to my team, would take a good project on herself but might think someone else couldn't handle the workload. I knew she was the only person really qualified though so I just emailed her occasionally during my ML saying, 'When I come back...' etc and asking her to keep me informed of things that were happening.
We needed a new member of staff while I was off but she didn't tell me our colleague had left and I found out from someone else, then she and my boss employed someone but she didn't give me his name or tell me anything about him until the week before I returned to work. She made the excuse that she had been busy and that is why she hadn't replied to my emails.
I returned to work a couple of months ago and the way things work at my job she has only just gone back down to her pre-cover pay. She has been complaining for ages about the fact she should have been promoted which I agree with and have done all I can in terms of emailing the relevant people but my boss has said that to do any more would be counter-productive.
She has been subtly implying things about the way I do things and pointed out a mistake I had made (which turned out not to be my mistake in any case) when it is something we all do wrong occasionally and part of the nature of the job. She told everyone in our departmental meeting that she had done a large part of my job while I was away and when I checked it it needed a lot doing to it. It might be that her methods differ from mine but there were spelling mistakes too.
While I was on ML she also took on a house for which she can't afford the rent without being on my salary, which makes me think she was just counting on my not coming back.
I have seen her have a bad attitude with other people, verging on rudeness but it is subtle enough and could just be read as feeling strongly about things.
Then I found out that our boss's boss has asked her to lead a big project. I am fine with it as I think they are doing it to appease her as she hasn't been promoted and it is not something I would enjoy doing anyway. What rankles is that if she was in my position she wouldn't want someone she managed to have that opportunity and she even said in interview that she wouldn't let them take on too much and then in the next breath was very enthusiastic to do loads of things. No-one else on the interview panel could see anything wrong with it.
Sorry to go on, and on, and on but I don't know how to handle the situation. It is so subtle that to blatantly say anything would just be overkill. I have in the past emailed my boss saying that I had found mistakes in the thing she said she had done and that was why it wasn't quite finished. And I have said to her in the past not to take on too much (she looked a bit bemused). I guess I just want some pointers on how to deal with her passive aggressiveness.