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.
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It comes after the collapse of BHS in 2016 with a £571 million deficit in its pot for 19,000 pension holders.