Search for the Decay $K_L \to π^0 μ^+ μ^-$

We report on a search for the decay \klpimumu carried out as a part of the KTeV experiment at Fermilab. This decay is expected to have a significant $CP$ violating contribution and a direct measurement will either support the CKM mechanism for CP violation or point to new physics. Two events were observed in the 1997 data with an expected background of $0.87 \pm 0.15$ events, and we set an upper limit \BR{\klpimumu} $ <3.8 \times 10^{-10}$ at the 90% confidence level.