  We report on a search for a bound di-neutron by comparing electron-induced
proton-knockout $(e,e'p)$ measurements from Helium-3 ($^3$He) and Tritium
($^3$H). The measurements were performed at Jefferson Lab Hall A with a 4.326
GeV electron beam, and kinematics of large momentum transfer $Q^2 \approx 1.9$
(GeV/$c$)$^2$ and $x_B>1$, to minimize contributions from non quasi-elastic
(QE) reaction mechanisms. Analyzing the measured $^3$He missing mass
($M_{miss}$) and missing energy ($E_{miss}$) distributions, we can distinguish
the two-body break-up reaction, in which the residual proton-neutron system
remains bound as a deuteron. In the $^3$H mirror case, under the exact same
kinematic conditions, we do not identify a signature for a bound di-neutron
with similar binding energy to that of the deuteron. We calculate exclusion
limits as a function of the di-neutron binding energy and find that, for
binding equivalent to the deuteron, the two-body break-up cross section on
$^3$H is less than 0.9% of that on $^3$He in the measured kinematics at the 95%
confidence level.
