I wish to relinquish my next of kin rights, is that possible.

You may not have any rights to property in your father's estate.  Do you know if he left a Last Will?  He could have written you OUT of a property bequest, so you'll need to see the Will.

If he didn't leave a will, then YES you can walk away from any property that he owned at his death.  You'll need to give the estate administrator a form called "Election" showing that you are freely and voluntarily waiving your right to any inheritance from your father's estate.  You should have an attorney write that waiver for you.

I am a lawyer in CT and practice in this area of the law.  I suggest writing a letter that is notarized and sworn to under oath that you are disclaiming your inheritance rights.  File the letter with the probate court and send copies to your grandma.

I am not admitted In Washington.  I am sorry for your loss. 

Besides the above there might be forms from the probate court that you can use and you should go down and ask the clerk in the county in which your father lived at the time of his death.  There may be a procedure they want.