It is understood the incident took place in the Wavertree area of the city earlier this month.
A spokeswoman for Merseyside Police said: "I can confirm a 24-year-old man, from Widnes, was arrested on suspicion of causing criminal damage and assault.
"He has been bailed until May pending further inquiries.''
The 24-year-old is no stranger to controversy. In February, Portsmouth fans complained after he allegedly made an obscene gesture towards them during a match at Fratton Park.
He was fined by the FA after dropping his shorts and baring his bottom at Everton fans in October.
Barton was sent home from a pre-season tour of Thailand after becoming involved in a brawl with a schoolboy Everton fan.
He was also fined six weeks' wages by his own club after stubbing a cigar out in the eye of young City team-mate Jamie Tandy at a club Christmas party.