  We present the results of three-dimensional femtoscopic analyses for charged
and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$
= 2.76 TeV. Femtoscopy is used to measure the space-time characteristics of
particle production from the effects of quantum statistics and final-state
interactions in two-particle correlations. Kaon femtoscopy is an important
supplement to that of pions because it allows one to distinguish between
different model scenarios working equally well for pions. In particular, we
compare the measured 3D kaon radii with a purely hydrodynamical calculation and
a model where the hydrodynamic phase is followed by a hadronic rescattering
stage. The former predicts an approximate transverse mass ($m_{\mathrm{T}}$)
scaling of source radii obtained from pion and kaon correlations. This
$m_{\mathrm{T}}$ scaling appears to be broken in our data, which indicates the
importance of the hadronic rescattering phase at LHC energies. A
$k_{\mathrm{T}}$ scaling of pion and kaon source radii is observed instead. The
time of maximal emission of the system is estimated using the three-dimensional
femtoscopic analysis for kaons. The measured emission time is larger than that
of pions. Our observation is well supported by the hydrokinetic model
predictions.
