Expressing brief condolences is appropriate.

I believe the following expressions are wildly inappropriate: assuming things about diseased and yours relationships, criticize the diseased, make assumptions about your grief, telling you why you feel certain way or how you should be grieving, prying for details, going on and on about your loss despite being asked to stop, sending inappropriate cards, making your loss about them (“I know how you feel because I lost insert... dog, squirrel, random person”) etc etc

Briefly stating sorry for your loss is perfectly fine