UK Police Certificates

Here's what the US Embassy in London website about Police Cert requirements:

Police Certificate for the United Kingdom

An immigrant visa applicant who has resided in the United Kingdom for 6 months or more since the age of 16, is required to obtain a police certificate from the Association of Chief Police Officers (ACPO). Further information is available from their website at ACPO . This police certificate will serve to advise the U.S. Embassy, London whether or not any criminal conviction is held against him/her. The police certificate will be sent to the address provided at the time of application. Please note that the Immigrant Visa Unit considers the police certificate valid for 12 months from the date of issuance, not six months as stated on the certificate.

Scotland

Despite the fact that the ACPO states that it's juristiction is only England, Wales and Northern Ireland, it does in fact cover Scotland too. If you live or have lived in Scotland this is the cert you need.

Your Record

If you have a clear record you should expect the report to say no more than 'No Trace'.

No Live Trace - this means that you have a spent conviction. It is recommended that you get a subject access from here before interview. Court and prison records may be required.

Convictions - court and prison records will be required, as applicable.

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You can find other UK specific information in the UK FAQ and the VJ UK Forum.