Is it permissible to use the police to steal some property, given that the country where the theft occurred does not rule according to what Allah has revealed?

It is not permissible to seek judgment from other than what Allah has revealed. The police are an executive, not a judicial, body, so it is permissible to seek their assistance to identify a thief. If it is impossible to repel injustice or secure a right except through the police, then there is no sin upon the one who seeks their help, even if they carry out procedures not approved by Islamic law, provided that one's heart dislikes the rule of conflicting man-made laws. It is not permissible to seek judgment from man-made courts except out of necessity if no Sharia courts exist, and if a right cannot be obtained except through them, then there is no harm.