The investigation was prompted by a recent incident at a market in Moscow in which a police officer was seriously injured, RIA Novosti reported.
"In order to reveal corruption links in market trading, the Investigative Committee has been instructed to carefully check the legitimacy of refusals to initiate criminal investigations into offenses or idleness by law-enforcement and control agencies and local officials," Investigative Committee spokesman Vladimir Markin said in a statement.
"This relates not only to Moscow markets. Checks will be held across the country," he said.
In the Moscow incident, police officers were attempting to arrest a suspected sex offender at a market. The operation ended with a police officer suffering serious head injuries. Two other police officers are being investigated for their alleged failure to take action during the incident, investigators said.
Russian President Vladimir Putin criticized the incident Wednesday, saying, "The efforts being made are clearly not enough: either nothing happens or progress is unacceptably slow."