  We prove that an integral block of the category $\mathcal O$ of the
periplectic Lie superalgebra contains a non-semisimple Jantzen middle if and
only if it contains a simple module of atypical highest weight. As a
consequence, every atypical integral block of $\mathcal O$ does not admit a
Kazhdan-Lusztig theory in the sense of Cline, Parshall and Scott.
