  We have studied a mosaic of 1T-CrSe$_2$ single crystals using
$\beta$-detected nuclear magnetic resonance of $^{8}$Li from 4 to 300 K. We
identify two broad resonances that show no evidence of quadrupolar splitting,
indicating two magnetically distinct environments for the implanted ion. We
observe stretched exponential spin lattice relaxation and a corresponding rate
($1/T_1$) that increases monotonically above 200 K, consistent with the onset
of ionic diffusion. A pronounced maximum in $1/T_1$ is observed at the low
temperature magnetic transition near 20 K. Between these limits, $1/T_1$
instead exhibits a broad minimum with a remarkable absence of strong features
in the vicinity of structural and magnetic transitions between 150 and 200 K.
Together, the results suggest $^{8}$Li$^{+}$ site occupation within the van der
Waals gap between CrSe$_2$ trilayers. Possible origins of the two environments
are discussed.
