Consider the discussion on page 77 of James Lepowsky and Haisheng Li's Introduction to Vertex Operator Algebras and Their Representations. In particular, the authors state that
The operator product expansion notation...suggests the use of the contour integration technique...and in fact in the conformal field theory literature, this contour-deformation technique is indeed often used in conjunction with the operator product expansion.
I am looking for further references that discuss that connect this contour deformation with the operator product expansion. In particular, how does deformation of the contour depend upon whether or not we are dealing with a conformal field theory? Any explanation or reference would be appreciated.