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You aren't required to accept it and if it is addressed to him you may want to consider telling the postman to return it with the notation that the addressee is deceased.
As far as taxes you would only be potentially responsible for any taxes accumulated since your marriage, nothing from before you were married. Most of the time in situations like yours an accountant can file your return as married filing separately and then the estate can file a return for him and you can avoid any liability at all but that depends on the specific facts of your case.