  Linear polarization measurements have been performed for $\gamma$-rays in
$^{91}$Ru produced with the $^{58}$Ni($^{36}$Ar, $2p1n$$\gamma$)$^{91}$Ru
reaction at a beam energy of 111 MeV. The EXOGAM Ge clover array has been used
to measure the $\gamma$-$\gamma$ coincidences, $\gamma$-ray linear polarization
and $\gamma$-ray angular distributions. The polarization sensitivity of the
EXOGAM clover detectors acting as Compton polarimeters has been determined in
the energy range 0.3$-$1.3 MeV. Several transitions have been observed for the
first time. Measurements of linear polarization and angular distribution have
led to the firm assignments of spin differences and parity of high-spin states
in $^{91}$Ru. More specifically, calculations using a semi-empirical shell
model were performed to understand the structures of the first and second
(21/2$^{+}$) and (17/2$^{+}$) levels. The results are in good agreement with
the experimental data, supporting the interpretation of the non yrast
(21/2$^{+}$) and (17/2$^{+}$) states in terms of the $J_{\rm max}$ and $J_{\rm
max}-2$ members of the seniority-three $\nu(g_{9/2})^{-3}$ multiplet.
