Tweets sent on Monday night contained abusive messages and death threats, aimed at participants in the Benefits Street programme, according to police.
Superintendent Long said: "We are assessing a number of tweets which were posted last night and investigating whether or not any criminal offences have been committed."
Channel 4 said that if any tweets "cross the line into specific threats", Twitter and the police would be notified.
The broadcaster said that it had received around 100 complaints, while Ofcom is thought to have received a similar number from viewers concerned about the portrayal of people on benefits.
More top news
There was an "alarming" increase in the number of death sentences issued around the world last year, Amnesty International has said.
Paracetamol is ineffective at treating back pain, Australian researchers say.
Madonna says she still cannot bring herself to watch footage of the moment she fell on stage while performing at the Brit Awards.