Yes you can refuse to accept an inheritance. It is known as "renouncing" or "disclaiming" a gift. If you are named as a beneficiary in a Will, you can disclaim your inheritance. To do so, contact the executor as to your wanting to renounce your gift; then contact the attorney handling the probate about your wish; have the attorney prepare a disclaimer of your inheritance (a relatively simple form that is signed and dated by you before a notary); and have the document filed with the probate court.