In Oxford, the city's Building division reviews residential permit applications and issues permits, and the Engineering office approves permits for work in the right-of-way, the public land along the street. I won't guess whether your walk needs one. We check with the permit office for your address, city or county, before work starts, and if a permit is needed we do the paperwork and line up the inspections.
One soil analysis of Lafayette County rates the risk from expansive soil, clay that swells when wet and shrinks as it dries, as real but uneven, with most trouble on lots that drain poorly or were leveled by cutting and filling. Around Oxford, and out in Batesville and Holly Springs, the broken walks we replace usually sit on graded lots or near big trees, so that's where the prep goes deepest.