  This paper generalizes two facts about oriented 3d TFTs to the unoriented
case. On one hand, it is known that oriented 3d TFTs having a topological
boundary condition admit a state-sum construction known as the Turaev-Viro
construction. This is related to the string-net construction of fermionic
phases of matter. We show how Turaev-Viro construction can be generalized to
unoriented 3d TFTs. On the other hand, it is known that the "fermionic"
versions of oriented TFTs, known as Spin-TFTs, can be constructed in terms of
"shadow" TFTs which are ordinary oriented TFTs with an anomalous $\mathbb{Z}_2$
1-form symmetry. We generalize this correspondence to Pin$^+$-TFTs by showing
that they can be constructed in terms of ordinary unoriented TFTs with
anomalous $\mathbb{Z}_2$ 1-form symmetry having a mixed anomaly with
time-reversal symmetry. The corresponding Pin$^+$-TFT does not have any anomaly
for time-reversal symmetry however and hence it can be unambiguously defined on
a non-orientable manifold. In case a Pin$^+$-TFT admits a topological boundary
condition, one can combine the above two statements to obtain a
Turaev-Viro-like construction of Pin$^+$-TFTs. As an application of these
ideas, we construct a large class of Pin$^+$-SPT phases.
