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If funds (that were contributed without tax paid) from a 401K are transferred to a Roth IRA the total amount transferred will be taxed as ordinary income in the year of transfer. This is the same tax treatment as if the funds were converted from a traditional to a Roth IRA.
So, the 13K would be added to your usual 40K of income and be taxed about 15% or about $1950 more tax or less refund.
What will not occur with transfer to the Roth that will occur with a cash out is the additional ten percent early withdrawal penalty on the funds taken from the 401K.
That would be about $1300 less tax (assuming you do not meet any exception).
Moving the funds just to a traditional IRA will not incur any tax at this time and you would still be able to convert those funds to Roth IRA (or take out subject to penalty and tax) at a later time either in part or in full.
The best course is to speak with the financial institution that you have the Roth to arrange for the transfer (either to a traditional or Roth IRA). My personal experience was that the amount of time and effort was about the same to transfer to either type of account.
Please ask if you need more information.