A possible answer extracted from https://ncatlab.org/nlab/show/quantization+of+3d+Chern-Simons+theory

The 3d TQFT candidate for quantum CS theory in the form of the Reshetikhin-Turaev construction and the corresponding modular tensor category data is discussed in

Reshetikhin; Turaev, Invariants of 3-manifolds via link polynomials and quantum groups. Invent. Math. 103 (1991), no. 3, 547–597.

B. Bakalov & Alexandre Kirillov, Lectures on tensor categories and modular functors AMS, University Lecture Series, (2000)

Stephen Sawin, Quantum groups at roots of unity and modularity J. Knot Theory Ramifications 15 (2006), no. 10, 1245–1277 (arXiv:0308281)

Victor Ostrik, MO comment August 2014