  We investigate the response to modular transformations and the fractional
statistics of Abelian multi-component fractional quantum Hall (FQH) states. In
particular, we analytically derive the modular matrices encoding the statistics
of anyonic excitations for general Halperin states using the conformal field
theories (CFTs). We validate our theory by several microscopic examples,
including the spin-singlet state using anyon condensation picture and the
Halperin (221) state in a topological flat-band lattice model using numerical
calculations. Our results, uncovering that the modular matrices and associated
fractional statistics are solely determined by the $K$-matrix, further
strengthens the correspondence between the 2D CFTs and (2+1)D topological
orders for multi-component FQH states.
