Six people were arrested during the referendum ballot and count for offences including alleged breach of the peace and assault.
Police Scotland said there were "isolated incidents" around the country during the process, which started at 7am yesterday and concluded this morning.
Assistant Chief Constable Bernard Higgins praised and thanked members of the public for their help and co-operation during the referendum campaign and ballot.
He said: "It is to everyone's credit that they remained calm on a day of potentially high emotion and co-operated fully with our police officers and also the staff at polling places on a day when record numbers turned out to vote.
"This meant the ballot and count passed off smoothly and there were just a very few isolated incidents across the country involving a small number of alleged offences.
"Police Scotland had plans in place to ensure the safety and security of the referendum and these worked.
"I would also like to thank our police officers across the country for the hard work and effort they put in to ensure the day went well."
He said that the six arrests were mainly for alleged breaches of the peace and assaults.
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