  We study the topological entanglement negativity between two spatial regions
in (2+1)-dimensional Chern-Simons gauge theories by using the replica trick and
the surgery method. For a bipartitioned or tripartitioned spatial manifold, we
show how the topological entanglement negativity depends on the presence of
quasiparticles and the choice of ground states. In particular, for two adjacent
non-contractible regions on a tripartitioned torus, the entanglement negativity
provides a simple way to distinguish Abelian and non-Abelian theories. Our
method applies to a Chern-Simons gauge theory defined on an arbitrary oriented
(2+1)-dimensional spacetime manifold. Our results agree with the edge theory
approach in a recent work (X. Wen, S. Matsuura and S. Ryu, arXiv:1603.08534).
