The Quark Gluon Plasma (QGP), a state of matter in which deconfinement and chiral symmetry restoration occur, can be produced by ultra-relativistic heavy-ion collisions. This state of matter is of great interest because in QGP, the colored quarks and gluons, fundamental entities in matter whose interactions are governed by the Quantum ChromoDynamics (QCD), can exist as a fluid over an extended volume much larger than the size of nuclei. The Chiral Vortical Effect (CVE) is a QCD phenomenon related to the quark chirality arising from the topological sector of the QCD and the large vorticity of the QGP created. The search for quark chirality effects has been a major scientific objective at RHIC. \The Solenoid Tracker at RHIC (STAR) detector, located at the Relativistic Heavy-Ion Collider (RHIC) in the Brookhaven National Laboratory (BNL), provides the experimental capability needed to probe the QGP, with the particle tracking and identification abilities built into the different parts of the detector. This thesis focuses on the search for the CVE with STAR data from Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 27 GeV and 19.6 GeV, from Run 2018 and 2019, repsectively. \ In order to search for the CVE, measurements of the correlations of the azimuthal angles between baryons, $\Lambda$ and protons, were made, in the form of observables $\gamma_{112} \equiv \langle \cos(\phi_{\alpha} + \phi_{\beta} - 2\Psi_{RP}) \rangle$ and $\gamma_{132} \equiv \langle \cos(\phi_{\alpha} - 3\phi_{\beta} + 2\Psi_{RP}) \rangle$, in which mathematically the CVE effects would be made manifest. $\alpha$ and $\beta$ represent the charge of the correlated particles, and to reduce the background, we take $\Delta\gamma \equiv \gamma_{OS} - \gamma_{SS}$, where we subtract the measurement of the correlation of pairs of same charge particles (SS) from that of opposite charge particles (OS). The KFParticle package was used for the reconstruction of the $\Lambda$ particles. To have a better interpretation of the results, the observables $\kappa_{112} \equiv \Delta\gamma_{112} / (v_{2}\cdot\Delta\delta)$ and $\kappa_{132} \equiv \Delta\gamma_{132} / (v_{2}\cdot\Delta\delta)$ were computed that allows for comparison across different systems. Specifically, these observables were compared with data generated from the A Multi-Phase Transport Model (AMPT) simulations. \ In addition, the flow-related background was also something that needed to be dealt with to get a clearer signal from the $\Delta\gamma_{112}$ and $\Delta\gamma_{132}$ observables. The Event Shape Selection method was applied in order to project the events to zero flow, attempting to reduce the flow-related background as much as possible. The Event Plane Detector (EPD) event plane was used as well to reduce the non-flow backgrounds. \ Our search yielded no definitive observation of the proposed CVE signal. We obtained an upper limit on the CVE signal from Au+Au collisions at 19.6 GeV and 27 GeV energies. Because of large statistical errors due to limited number of $\Lambda$ per event, the obtained upper limit is not very stringent. We will also discuss a possible effect due to the presence of baryon annihilations and the future direction of CVE searches. Large statistical data sets will be critical for those efforts.