It is well known that a torsion free sheaf is also locally free on a curve, in the algebraic geometry category. A further fact is that a torsion free sheaf is locally free outside a Zariski closed subset of codimension $\geq 2$ on a higher dimension normal variety. Those results can be found in Proposition 5.1.6 or Proposition 5.1.7 in the book Introduction to Singularities Shihoko Ishii, https://link.springer.com/content/pdf/10.1007%2F978-4-431-56837-7.pdf
My question: can those results still hold in the analytic setting?