Laurent series for functions with branch singularities

Question

I'm trying to derive a form of the indentation lemma for a function of the form, say, $f(z)=\frac{h(z)}{\sqrt{z^2-k^2_0}}$, where $h(z)$ is analytic, and $k_0$ is some possibly complex number. As such, I was wondering if it were possible to express this series in terms of a Laurent series? As I am not very clear on this topic, it seems that expanding the denominator in a Taylor series gives a set of terms with fractional powers, and use of Cauchy's integral formula does not seem possible due to the branch cut. As such, I was wondering how to proceed.