The $\Lambda^0$ hyperons have an interesting property that they can be produced polarized in collisions of unpolarized particles, as was discovered in Femilab in the 70's. Since then, the $\Lambda^0$ polarization has been measured in a variety of collision systems, including $e^+$+$e^-$. Most of the measurements indicate that the polarization originates from final state effects, such as fragmentation and hadronization. It is therefore important to investigate if there is any contribution of initial state effects to the polarization, such as spin-spin correlation of initial state partons. This is possible utilizing a newly proposed experimental method which measures spin-spin correlations of $\Lambda^0$ hyperon pairs.

In these proceedings, we present preliminary results from the first experimental measurement of spin-spin correlations of $\Lambda^0\bar{\Lambda}^0$, $\Lambda^0\Lambda^0$, and $\bar{\Lambda}^0\bar{\Lambda}^0$ pairs in $p$+$p$ collisions at $\sqrt{s} = 200\,\mathrm{GeV}$ measured by the STAR experiment. The spin-spin correlation is measured to be consistent with zero for all three $\Lambda^0$ hyperon pair combinations, within the uncertainties. This measurement provides the first limit on the $\Lambda^0$ hyperon pair spin-spin correlations in $p$+$p$ collisions at $\sqrt{s} = 200\,\mathrm{GeV}$.