We consider the second order difference equation ψ(z + h) + ψ(z - h) + v(z)ψ(z) = 0 where z is a complex variable, h > 0 is a parameter, and v is an analytic function. As h → 0 the analytic solutions to this equation have quasiclassical behavior. In this note we describe their uniform asymptotics in neighborhoods of simple turning points, the neighborhoods being independent of h.