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
Andy Murray is Britain's last hope of a 2015 Wimbledon win after overcoming an apparent shoulder injury to beat Italy's Andreas Seppi.
New Tour de France time-trial record set after Australian Rohan Dennis raced into the lead during Stage one of the competition.
Fresher and cooler as we head into the second half of the weekend.