<p>Spin-orbit interactions cause a global polarization [P] of Lambda (anti-Lambda) hyperons with the vorticity (or total angular momentum) in the participant collision zone. The strong magnetic field mainly created by the spectator protons would split the Lambda and anti-Lambda global polarization [Delta P]. Quantum chromodynamics (QCD) predicts topological charge fluctuation in vacuum, resulting in a chirality imbalance, or parity violation in a local domain. This would give rise to an imbalanced left- and right-handed Lambda (anti-Lambda) [Delta n], as well as a charge separation along the magnetic field, referred to as the chiral magnetic effect (CME). The latter can be characterized by the parity-even [Delta gamma] and parity-odd [Delta a1] observables. While measurements of the individual [Delta P], [Delta gamma], and [Delta a1] have not led to affirmative conclusions on the CME or the magnetic field, correlations among these observables may reveal new insights. We report exploratory measurements of event-by-event correlations between [Delta P] and [Delta gamma], and between [Delta n] and [Delta a1] by the STAR experiment in Au+Au collisions at 27 GeV. No correlations have been observed beyond statistical fluctuations. Future endeavor would be to extract an upper limit from the data as well as to apply the correlation analysis to other data samples.</p>