The leaflets, which are also thought to have been distributed nationally, were pushed through the letterboxes of homes in and around the Brinsley area.
Inspector Mike Ebbins, neighbourhood inspector for the Broxtowe borough, said officers were taking local residents' concerns seriously after receiving a number of reports.
The matter has been recorded as a hate incident and officers are now examining the leaflets to see if a criminal offence had taken place.
He said: "Nottinghamshire Police take a zero-tolerance approach to all hate crime which can have a devastating impact upon individuals and communities.
“We treat all reports seriously and they will be thoroughly investigated.
"If anyone else has concerns about the leaflets or extremist content please speak to our neighbourhood team.
"Nottinghamshire is a diverse and tolerant county and as a police service we are absolutely committed to ensuring that everyone is treated equally and has the same opportunities as everyone else to be part of our communities."
Anyone who is affected by hate crime can report it by calling Nottinghamshire Police on 101.