  We show that multiband superconductors with broken time-reversal symmetry can
produce spontaneous currents and magnetic fields in response to the local
variations of pairing constants. Considering the iron pnictide superconductor
Ba$_{1-x}$K$_x$Fe$_2$As$_2$ as an example we demonstrate that both the
point-group symmetric $s+is$ state and the C$_4$-symmetry breaking $s+id$
states produce in general the same magnitudes of spontaneous magnetic fields.
In the $s+is$ state these fields are polarized mainly in ab crystal plane,
while in the $s+id$ state their ab-plane and c-axis components are of the same
order. The same is true for the random magnetic fields which are produced by
the order parameter fluctuations near the critical point of the time-reversal
symmetry breaking phase transition. Our findings can be used as a direct test
of the $s+is/s+id$ dichotomy and the additional discrete symmetry breaking
phase transitions with the help of muon spin relaxation experiments.
