You have my condolences
That's a perfectly acceptable response....perhaps you could also ask what you can do for her?
I am certain you have experienced a loss of a loved one in your life so you can imagine her pain. Of course tell the person you feel sorrow for her loss and you can also tell her she is in your thoughts.
I am very sorry for your loss. loosing a parent is one of the most difficult losses we face in life. I am offering my prayers to you and your family. Take joy in the memories of your dad, they will help heal your heart.
"I'm very sorry to hear about your loss thinking of you and wishing you strength in the coming days."
Nobody is good at this stuff.
That the proper response. Then you have to figure out if you need to do something, by asking her about if she was leaving town and such so you can know what effects this might have on whatever you are working on with her.
That is all you can say since you are not close to her.
"I'm so sorry to hear of your loss. My thoughts (and prayers? depending on if you pray or not) are for you and your family."
If you're only on a professional basis with them, I'd think that would be enough.
Yeah that's perfect!