The authorities in St Kitts hires an international due diligence agency to conduct background checks and they liaise with the local authorities in each country so the process is very thorough. There is a high probability that your minor offenses will be discovered in the due diligence process.
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What due-diligence standards are there for investment immigrants to St. Kitts and Nevis?
What kind of background checks are there? I had several minor traffic convictions in my home country.