In general, the acceleration vector for planar motion in polar coordinates is given by $$\mathbf a=(\ddot r-r\dot\theta^2)\hat r+(r\ddot\theta+2\dot r\dot\theta)\hat\theta$$
Although you don't say it, I assume you are asking about circular motion where $\dot r=\ddot r=0$, so that the centripetal acceleration becomes $$a_r=r\dot\theta^2$$ and the tangential acceleration becomes $$a_\theta=r\ddot\theta$$
Therefore, one could argue that these values are related through the $r$ variable such that $$\frac{a_r}{\dot\theta^2}=\frac{a_\theta}{\ddot\theta}$$
Of course, if there is no tangential acceleration for our circular motion we get an undefined value mathematically, but this makes sense physically. You can have any centripetal acceleration for uniform circular motion.
Note that the angular acceleration is just $\ddot\theta$, so if you want to bring that in too then that is a pretty simple thing to do.