When users make personal privacy choices, correlation between their data can cause inadvertent leakage about users who do not want to share their data by other users sharing their data. As a solution, we consider local redaction mechanisms. As prior works proposed data-independent privatization mechanisms, we study the family of data-independent local redaction mechanisms and upper-bound their utility when data correlation is modeled by a stationary Markov process. In contrast, we derive a novel data-dependent mechanism, which improves the utility by leveraging a data-dependent leakage measure.