My understanding is that a person would not be nicked by the police or anyone else, but an item would be nicked by a thief.
She nicked the platter. <-- She stole the platter.
The platter was nicked. <-- The platter was stolen.
He was busted by the police. <-- Informal usage.
He was caught by the police. <-- Formal usage
He was arrested by the police. <-- Another good option for formal use.