Print manager Communisis lists Skipton as a client on its website. However, it is not known whether Communisis was involved in the printing error.
Both Skipton and Communisis chief executive Andy Blundell declined to comment.
The building society has apologised for the error and offered to change the account number of any customers seeking peace of mind.
A spokeswoman for Skipton said the printing error did not include the other customers' address, date of birth or other identifying details, and so not enough details were revealed to put accounts at risk.
She said: "The risk to affected customers is negligible because of this.
"Nevertheless, we have written to those affected to apologise and to reassure them that the correspondence contained insufficient information to enable any unauthorised transactions on their accounts."
Print error hits building society customers
A third-party "printer error" has exposed the details of 3,115 Skipton Building Society customers, with names and account balance printed on the back of other people's statements.
