Before you put your coworker’s email address on your out-of-office message, get their approval and discuss a plan for handling requests and passing responsibilities back when you return.
But what if you’re only taking off one day? Sometimes, it might seem silly to bother with an out-of-office for such a short amount of time–especially if it’s a day that a lot of other people are taking off (such as a national holiday). If people do need you to get back to them urgently, they’ll think they’re being ignored. (Even if you define “urgently” differently.) And if there’s a chance of an emergency landing in your inbox, it’ll be that much harder for you to unplug because you’ll just keep “checking in.”

I wrote the above comment off the top of my head. I wish I had time to rewrite and edit it. I would have changed “their goldfish” to “a spider they accidentally stepped on”, and would have added more detail to the story of the sister’s death (e.g. “her Pomeranian yapping” rather than the less descriptive “her dog barking”). Unfortunately, I could not do the thorough writing job required for that comment because someone close to me recently … – The person whose out of office advertised his gig on the weekend, for anyone in travelling to [city] – The people in a certain department who have taken to saying things like “if you really need to contact me, call 000-YYY-XXXX where Y is the square root of [insert numbers] and X is the year plutonium was discovered.” – The ones where people have an auto response saying they only check their emails once a day between 1-2pm – “I’m on research leave and I may be slow to reply.” (Whereby it is guaranteed they will reply immediately, because academics do not *really* take breaks).
She definitely had an excessive ego, and she was also a narcissist who loved to micromanage so it was a really toxic place under her. We used to love it when she went on vacation because the office was quiet, calm, and drama-free.