The paper was published by the Association of Chief Police Officers who spoke to detectives and community officers throughout the country.
The report said: "While overall this country has accommodated this huge influx with little rise in community tension, in some areas sheer numbers, resentment and misunderstanding, have created problems."
However, the paper said new migrants were more likely to commit certain offences, and had caused tensions in some areas because of their arrival in unexpectedly large numbers.
Polish migrants were said to be linked to drink-driving offences, while there had been problems in London with Romanian adults using children for petty robberies.
Peter Fahy, chief constable of Cheshire constabulary and co-author of the report, said: "Migration has had a significant impact on UK communities in past years but while this has led to new demands made on the police service, the evidence does not support theories of a large-scale crime wave generated through migration.
"In fact, crime has been falling across the country over the past year. Many migrants are young professionals looking to earn money and return to their home countries. Cultural differences such as attitudes to offences like drink driving may exist, but can be exaggerated."
The report said the areas facing most difficulties included Cambridgeshire and Lincolnshire, where migrant workers were attracted by local farm work.
A number of police forces have called for more money to deal with the extra demands posted by the increase in local population.
Fahy said: "Better forecasting and data-sharing between local agencies to pick up changes in local populations quicker is necessary to help anticipate the issues."