If you were finger-printed in connection with the arrest, it is likely that the arrest info (including the charge on which the arrest was made) is in the state and FBI criminal records data-base. Those records will show that no charges were brought. Not all potential employers have access to arrest records and many are prohibited by state law from asking about arrests not leading to conviction. Be very exact in reading and answering specific questions on job applications. You can order up a copy of your own criminal history records from both your state's data-base and the FBI.
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There is a huge difference between being arrested, charged, and convicted. You can check the court records online on the Washington Courts website. http://dw.courts.wa.gov/index.cfm?fa=home.home
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Private employers will only be provided "conviction data" by the Washington State Patrol Identification section. This is the typical "background check."
However, some employers hire a private firm to check court records, which can show charges that did not result in conviction.
The term "convicted" means having been found guilty by a court, or having entered a plea of guilty. Clearly an arrest, or even being charged, is not a "conviction."