  The limit point and limit circle classification of real Sturm-Liouville
problems by H. Weyl more than 100 years ago was extended by A.R. Sims around 60
years ago to the case when the coefficients are complex. Here, the main result
is a collection of various criteria which allow us to decide to which class of
Sims' scheme a given Sturm-Liouville problem with complex coefficients belongs.
This is subsequently applied to a second order differential equation defined on
a ray in $\mathbb C$ which is motivated by the recent intensive research
connected with $\mathcal P \mathcal T$-symmetric Hamiltonians.
