We present a search for a neutral particle, pair produced in $p\overline{p}$ collisions at $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$, which decays into two muons and lives long enough to travel at least 5 cm before decaying. The analysis uses $\ensuremath{\approx}380\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ of data recorded with the D0 detector. The background is estimated to be about one event. No candidates are observed, and limits are set on the pair-production cross section times branching fraction into dimuons $+$ $X$ for such particles. For a mass of 10 GeV and lifetime of $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{s}$, we exclude values greater than 0.14 pb (95% C.L.). These results are used to limit the interpretation of NuTeV's excess of dimuon events.