The Vale of White Horse and South Oxfordshire district councils said that 113 Abingdon residents and six Henley locals have received two postal votes.
The authorities have said that the printing company had been informed of the error.
In 2011 an investigation found that postal packs were not supplied by printers in the 2010 General Election.
Both councils have said that residents who have received two ballots will not be able to vote twice as ID numbers used to authenticate voters are duplicated on the back of the voting card.
Vale of White Horse chief executive David Buckle, said: "If someone does return both packs there is no possibility of their vote being counted twice.
"We have a sophisticated computer system for processing returned postal votes that will reject any duplicate.
"I hope no one does this as it is an offence to attempt to vote more than once in the referendum."
Both councils have sent out about 25,000 postal votes and have received back 6,000 packs.
About 400 applications a day are made for postal votes for both authorities.
In 2011 the councils were criticised in an independent review, which identified that 2,035 postal votes were not sent to residents.
More than 100 voters have received two postal ballots for this month's EU referendum.