Unfortunately, as an AI language model, I cannot guarantee the absolute accuracy of the information I provide. Nevertheless, here are five interesting events that happened on or around June 27 in Tennessee history:

1. In 1949, Mildred Jeter and Richard Loving, an interracial couple from Virginia, traveled to Washington D.C. to get married. When they returned to Virginia, they were arrested and sentenced to a year in jail for violating Virginia's anti-miscegenation laws. However, their case eventually went all the way to the Supreme Court, which struck down such laws nationwide. Their story inspired the movie "Loving," which was partially filmed in Tennessee in 2015.

2. In 1921, a race riot erupted in Tulsa, Oklahoma, leaving hundreds of African Americans dead and thousands homeless. Many of the displaced residents ended up in other cities, including Nashville, where they faced discrimination and hostility from the white community. The event is often cited as one of the worst instances of racial violence in American history.

3. In 1968, civil rights leader James Meredith started a solo march from Memphis, Tennessee to Jackson, Mississippi, to promote voter registration among African Americans. However, on the second day of his journey, Meredith was shot and wounded by a white supremacist. Despite his injuries, he managed to complete the march later that year.

4. On June 27, 1985, a bomb exploded at the Rainbow Terrace Apartments in Chattanooga, killing five people and injuring dozens more. The attack was later traced to white supremacist groups affiliated with The Order, a far-right organization that espoused racist and anti-Semitic views. Several members of the group were eventually arrested and convicted for various crimes.

5. In 1870, the state of Tennessee was readmitted to the Union after having seceded during the Civil War. The state had been under military control for several years and had been forced to ratify the 14th Amendment, which granted citizenship to all persons born or naturalized in the U.S. and prohibited states from depriving anyone of due process or equal protection under the law.