Have the police said the following to you (or your wife):
You are under arrest for xxxxxxx, you have the right to remain silent, but if you don't, your words can and will be used in the court of law against you ?
If you heard those words, congratulations, you have been arrested. Otherwise you haven't.
But stop worrying. ONLY a conviction of a crime that are punishable for 5 years in prison or up will result in the failure of background check. So your immigration application is safe.