Although saddened that a loved one is gone, most people are not going to turn down an inheritance. There are, however, reasons why you may want to do just that.  If you do decide you do not want an inheritance, you may have to submit the proper paperwork to a probate court and/or the Internal Revenue Service to properly disclaim an inheritance.
A sudden windfall can present problems. For some, it can cause disqualification for much needed programs such as Medicaid or SSI. If the decedent failed to create an estate plan that considered the tax ramifications of the gift, that can also create a problem. An individual, for example, may inherit from a deceased spouse.  This gift may not be subject to a federal estate tax due to the unlimited marital deduction, but the receipt of the deceased spouse share of their estate may cause the surviving spouse's  estate to be subject to the federal estate tax at the death of the second spouse. By disclaiming the inheritance, the assets may pass to an exmpet trust established for the benefit of surviving spouse or if the couple did not have a trust to the next in line to inherit, often a child.  In either event, the disclaimed funds would not be subject to estate tax at the death of the  second spouse.
If you find yourself in a position where your estate may be subject to estate taxes at your death talk to a qualified estate planning attorney before you accept more assets from another estate to see whether discliaiming is a viable option.