A month after announcing that two Shelby County schools were under investigation for potential cheating on state achievement tests, the Tennessee Department of Education has cleared them.

The state investigated 2013-2014 TCAP results at Alcy and LaRose elementary schools in Shelby County Schools, as well as results in Robertson and Williamson counties. Shelby County Schools received the audit results on Thursday. Williamson County Schools also has been cleared in the investigation.

The districts were flagged after the state did an erasure analysis, which analyzes the percent of answers changed from wrong to right on the multiple-choice exam. Officials hired psychometricians to examine the three districts where small groups of students had frequently changed answers.

“We were confident the state’s investigation would mirror our internal investigation, showing our testing integrity had not been compromised, and that our schools are clear of wrongdoing,” the Memphis district said in a statement. “We’re proud of the hard work of our students and educators.”

Though state officials have been analyzing erasure marks since the 2011-2012 tests, this was the first time they shared the results with districts, in an effort to help administrators examine their testing security protocols.

Beginning next school year, Tennessee students no longer will take tests that are entirely multiple choice. The new TNReady assessment, which will be mostly online, incorporates open-ended questions in addition to traditional multiple-choice test items. Test results for the 2014-15 school year were released Wednesday.