Sure, that would be a logical first question. I don't believe though it was the only question that could have been asked in that situation.
Just for the sake of argument, let's say Cooper's death was accidental, Harris had just found him dead, he thinks his wife will never forgive him, he knows he'll never forgive himself, and on top of all that, LE is definitely treating him like a suspect.
I'm not sure any question he could have asked would sound OK to most folks. I think most of us think we would be so overcome with grief that we'd be incapable of speaking at all. I think that of myself for sure.
But. I'm not Harris, have no clue who he is, or how he responds to anything, and unless he is a sociopath, I think it's very likely he was in some kind of shock at that point.