> ADDED: You're probably going to end up lying or at least being very vague "some family stuff to take care of" in this specific scenario but for one month that didn't trigger reporting to employer a lot of professionals could probably get off with it. In any case, the GPT answer seems totally correct for the parameters given.
Where I live that is subject to cancellation of the work contact, you can't lie about why you are absent though the imprisonment can't be cause by itself for laying off.
Maybe you're talking about something else but for standard PTO/vacation that I'm owed it would seem absurd if I had to justify how I was going to spend my time off. It's none of your business.
Obviously not talking about standard PTO/vacation.
Where I live you must inform your employer unless you are lucky enough to have enough PTO/va. to spend your PTO/vacation in prison and hide it from your employer. But even then I don't think that will work out because there are administrative stuff related to social welfare you have to comply to and at some point it will be on your employer's radar anyway (why is that guy exempt from social welfare taxes for that specific month ? and why did the police asked me to confirm he was working here ? etc.).
BUT in practice, until recently, if imprisonment is less than 3 years then you won't spend a day in prison (unless you are deemed too dangerous). But then you have an electronic bracelet and other obligations that will at some point alert your employer.
I read now that prison time of any length will have to be spent in prison (no more less than 3 years or 2 years or 18 months pass). But for prison time less than 18 months you can have a bracelet on the first day.
All that to say I don't think it's manageable and possible to hide prison time from your employer, even if you have enough PTO/vac. days to cover for it.
Where I live that is subject to cancellation of the work contact, you can't lie about why you are absent though the imprisonment can't be cause by itself for laying off.