Quark interactions with topological gluon configurations can induce local chirality imbalance and parity violation in quantum chromodynamics, which can lead to the chiral magnetic effect (CME) -- an electric charge separation along the strong magnetic field in relativistic heavy-ion collisions. The CME-sensitive azimuthal correlator observable ($Deltagamma$) is contaminated by background arising, in part, from resonance decays coupled with elliptic anisotropy ($v_{2}$). We report here the first differential measurements of the correlator as a function of the pair invariant mass ($m_{rm inv}$) in 20-50% centrality Au+Au collisions at $sqrt{s_{_{rm NN}}}$= 200 GeV by the STAR experiment at RHIC. Strong resonance background contributions to $Deltagamma$ are observed. At large $m_{rm inv}$ where this background is significantly reduced, the $Deltagamma$ value is found to be also significantly smaller. An event shape engineering technique is deployed to determine the $v_{2}$ background shape as a function of $m_{rm inv}$. A $v_{2}$-independent signal, possibly indicating a $m_{rm inv}$-integrated CME contribution, is extracted to be $Deltagamma_{rm signal}$ = (0.03 $pm$ 0.06 $pm$ 0.08) $times10^{-4}$, or $(2pm4pm5)%$ of the inclusive $Deltagamma(m_{rm inv}>0.4$ GeV/$c^2$)$=(1.58 pm 0.02 pm 0.02) times10^{-4}$. This presents an upper limit of $0.23times10^{-4}$, or $15%$ of the inclusive result at $95%$ confidence level.