Syntactic characterisation of the intersection of CTL and LTL
Note that by "equivalent", we actually need to interpret LTL over trees. Thus, we say that a CTL formula $\phi$ is equivalent to an LTL formula $\psi$, if $\phi$ is equivalent to the CTL* formula $A\psi$.

Thus, we essentially compare LTL and CTL in the common grounds of CTL*.

Given this, it's not hard to construct a procedure to check the equivalent. Simply check whether the formula $\phi \iff A\psi$ is a tautology in CTL*. This can be done in 2EXPTIME. However, since satisfiability of CTL is only EXPTIME complete, it might be possible to reduce this to EXPTIME (but I haven't given it much thought).