We show that the pure mapping class group
N
g
k
\mathcal {N}_{g}^{k}
of a non-orientable closed surface of genus
g
⩾
2
g\geqslant 2
with
k
⩾
1
k\geqslant 1
marked points has
p
p
-periodic cohomology for each odd prime
p
p
for which
N
g
k
\mathcal {N}_{g}^{k}
has
p
p
-torsion. Using the Yagita invariant and cohomology classes obtained from some representations of subgroups of order
p
p
, we obtain that the
p
p
-period is less or equal than
4
4
when
g
⩾
3
g\geqslant 3
and
k
⩾
1
k\geqslant 1
. Moreover, combining the Nielsen realization theorem and a characterization of the
p
p
-period given in terms of normalizers and centralizers of cyclic subgroups of order
p
p
, we show that the
p
p
-period of
N
g
k
\mathcal {N}_{g}^{k}
is bounded below by
4
4
, whenever
N
g
k
\mathcal {N}_{g}^{k}
has
p
p
-periodic cohomology,
g
⩾
3
g\geqslant 3
and
k
⩾
0
k\geqslant 0
. These results provide partial answers to questions proposed by G. Hope and U. Tillmann.