I do not believe it is possible to purge child support records. If you had a founded allegation through CPS - ie.. a finding after an investigation - there may be a way to litigate it or over turn it - however, you will need to determine if that is what exists and likely prove you had no notification of it - in order to contest it. You need to consult with an attorney ion a more lengthy setting than the internet.
I do not practice in Washington but have been keeping an eye on the issue you raise. You should talk with a CPS defense attorney to find out your statutory rights there and look at the articles I have linked below to see if you may need a broader challenge to Washington's CPS registries to get the relief you seek.
If you can prove the you were never notified of the original finding by CPS and your right to a due process hearing about the validity of the "charge", you have a better chance of undoing it than if there was a finding that you ignored at the time. The fact that you never had to go to court is irrelevant. CPS can conduct their investigations and make findings without ever taking a case to court.
A CPS finding that you have neglected your own children, unless it was life threatening neglect, should not interfere with a nursing career, though you may have to fight through a lot of bureaucratic red tape at each stage of your education, licensing and job placement process to have the 15 year old record be appropriately ignored.
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