Personally, I don’t send cards for sympathy, I hand-write short notes. I just think just merely signing my name to a pre-printed sentiment in a card, is almost literally the least I can do. So I’d send a personal note and also sign the office card.
If I am 100% honest, I’ll admit that I’m still somewhat new to all this. My parents never did anything like this so I never learned. They’re not very friendly people and I never went to a wake or a funeral in all my life before I moved out. (They only went when they were dragged). As an adult, I have been lucky to not have many people close to me die, but it means when someone does, I’m a little unsure of the protocol. I’ll sign the company card and send her a hand-written note on my own. Thanks!
Google “sympathy notes” - there is pretty much an established form for these things, and when you sit down in front of a piece of paper to write something like this, cribbing from the form is a good thing.
I doesn’t have to be more than three or four lines, though you can write more if you knew the deceased and have nice things to say about him or her. Just something like: “I was so sorry to hear about the loss of your [relative]. You always spoke so highly of him/her and I know you were close. [If you know the deceased personally, a couple lines here like ‘He was always so . . .’ or 'I remember when she . . . ’ If you can sincerely say that the deceased spoke highly of or truly loved the person you’re writing, that’s a very nice thing to add.] I hope you know that my thoughts [and prayers, if appropriate] are with you and your family during this difficult time. Please let me know if there is anything I can do for you.” Add an appropriate closing, from “yours sincerely” to “with much love,” depending on your relationship with the person you are writing.
I use only white or cream paper and blue or black ink. No pink ink, no hearts and balloons stationery. (Duh.) No business stationery, it’s not a work matter. Take five minutes to draft the note on scrap paper or the computer, copy it neatly on the paper and pop it in the mail. Maybe it’s wishful thinking on my part, but I do believe it is more meaningful for many people than a Hallmark card with just a signature on the bottom.
ETA: And I avoid saying (writing) “dead” or “death” or “died,” I use instead “the loss of” or “the passing of”. I know some might find that overly nice (maybe precious), but I don’t want DEAD to be the thing that leaps off the page at a bereaved reader.
It is unlikely in the extreme that anyone will check your office card for your name or the absense thereof. So signing that card in solidarity with your officemates need not have anything to do with whether you send a personal card or note outside the office.
Really, group cards for any occasion don’t take the place of individual cards, but seeing a whole bunch of signatures on them is still nice in that sense of “ooh, lookie, bunches of people like me, they signed my card”.