In this paper, we consider the state-dependent regime switching diffusion process \((X(t), R(t))_{t \geqslant 0}\) , where the drift term does not necessarily satisfy the dissipative condition for certain states of the switching component. We develop delicately the Lindeberg replacement trick and a change-of-measure technique to obtain the convergence rate between the law of \((X(t), R(t))_{t\geqslant 0}\) and that of its Euler-Maruyama scheme with constant and decreasing step sizes. This convergence rate is quantified in terms of a function-class distance \(d_{\mathcal {G}}\) . Moreover, we establish the ergodicity property of the Euler-Maruyama scheme. To illustrate our theoretical findings, we present in detail an example.
