On a smooth, bounded pseudoconvex domain
Ω
\Omega
in
C
n
\mathbb {C}^n
, to verify that Catlin’s Property (
P
P
) holds for
b
Ω
b\Omega
, it suffices to check that it holds on the set of D’Angelo infinite type boundary points. In this note, we consider the support of the Levi core,
S
C
(
N
)
S_{\mathfrak {C}(\mathcal {N})}
, a subset of the infinite type points, and show that Property (
P
P
) holds for
b
Ω
b\Omega
if and only if it holds for
S
C
(
N
)
S_{\mathfrak {C}(\mathcal {N})}
. Consequently, if Property (
P
P
) holds on
S
C
(
N
)
S_{\mathfrak {C}(\mathcal {N})}
, then the
∂
¯
\overline {\partial }
-Neumann operator
N
1
N_1
is compact on
Ω
\Omega
.