Everything sounds stiff and uncaring. Honestly, tell her that you heard, you're sorry for her loss and offer condolences. Don't agonize it, even a somewhat basic and wooden platitude like that has some meaning.
As someone who has experienced the loss of a loved one my condolences or my thoughts or prayers are with you is an appropriate response. It shows that you care but doesn't make any promises that are uncomfortable for promiser to keep. I have had people tell me that any time you need to talk let me know and they fell through on it and quite frankly I would have preferred three answers above then to have someone offer a listening ear and not follow through.
My condolences on the loss of your father.
A simple "Sorry to hear about your father" is a fairly widely-used comment to make in my experience, and seems to fit most circumstances. Depending on well she feels she knows you (and how she's feeling at the time) she may or may not want to talk about it, so don't push it if she just says something like "Thanks" and turns away. We all have our own way of coping with grief.
I would say that you're sorry for their loss, and, if you knew the deceased family member, and maybe have something to share with them that they would enjoy or appreciate, share it with them.
A close friend's mother died about a year ago, and while she was in the hospital, shortly before her death, I went to visit her, and we had a pleasant visit. None of the family was there at the time, so it was just the two of us.
When I left, I didn't mention it to my friend, but later, after her mother passed away, I mentioned the visit, and shared some of what we'd spoken about with her, and she appreciated knowing that I had gone, and knowing that we'd had a good visit and were able to spend some time together.
Sharing things like that, things that will comfort the family, even in some smalll way, matter.
I hope this helps.
From what I've learned so far in my "Death and Human Behavior" class, the best thing is to talk to them about it and be willing to listen to what they have to say. Death is normally an uncomfortable thing for people to talk about, so we naturally just want to say a few words and leave it at that. If she prefers not to talk about it then she will let you know, but some people find comfort letting it out or just simple conversation. If you just want to say something and leave it at that then just let her know that if she needs someone to talk to that you are available to do so, but that's just my opinion. I hope this helps, good luck.
Say nothing...Because nothing you say will make anyone feel better, except maybe " My prayers are with you"