  We have performed $^{27}$Al-NMR measurements on single-crystalline
UPd$_2$Al$_3$ with the field parallel to the $c$ axis to investigate the
superconducting (SC) properties near the upper critical field of
superconductivity $H_{\rm c2}$. The broadening of the NMR linewidth below 14~K
indicates the appearance of the internal field at the Al site, which originates
from the antiferromagnetically ordered moments of U 5$f$ electrons. In the SC
state well below $\mu_0H_{\rm c2}$ = 3.4~T, the broadening of the NMR linewidth
due to the SC diamagnetism and a decrease in the Knight shift are observed,
which are well-understood by the framework of spin-singlet superconductivity.
In contrast, the Knight shift does not change below $T_{\rm c}(H)$, and the NMR
spectrum is broadened symmetrically in the SC state in the field range of 3~T
$< \mu_0 H < \mu_0 H_{\rm c2}$. The unusual NMR spectrum near $H_{\rm c2}$
suggests that a spatially inhomogeneous SC state such as the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state would be realized.
