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
The Crown Prosecution Service says the internet has provided "new platforms for offending behaviour"
A Public Health England report estimated 150,000 to 200,000 Britons are infected with the virus by imported pork every year.
Tens of thousands of people have travelled to a sleepy town in the American west, to witness a rare celestial event.