I can speak from experience that the inbox is the property of the company. Worked at many company's who would commonly just disable the email account to login and forward all new email to a manager (or ceo/whatever).
This is also true with any computer that they gave you.
> I'm not a lawyer so I can't speak for the legality of this.
But if you are talking about a company's email server that you have an account on. It's the private property of the company likely.