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A key factor in assessing the success of a program that links released individuals to care is the time from release to receiving care in the community (linkage time). To estimate the linkage time, records from correction systems are linked to Ryan White Clinic data using encrypted Unique Client Identifier (eUCI). Most of the records that were linked using eUCI belong to the same individual; however, in some cases, it may link records incorrectly, or not identify records that should have been linked. We propose a Bayesian procedure that relies on the relationships between variables that appear in either of the data sources, as well as variables that exists in both to identify correctly linked records among all linked records. The procedure generates <jats:italic>K<\/jats:italic> datasets in which each pair of linked records is identified as a true link or a false link. The <jats:italic>K<\/jats:italic> datasets are analyzed independently, and the results are combined using Rubin's multiple imputation rules. A small validation dataset is used to examine different statistical models and to inform the prior distributions of the parameters. In comparison with previously proposed methods, the proposed method utilizes all of the available data and is both flexible and computationally efficient. In addition, this approach can be applied in other file linking applications. 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