Array-reader based two-dimensional magnetic recording (TDMR) is considered as a key technology for next-generation magnetic recording due to its advantages such as diversity gain against noise and inter-track interference suppression. In this work, a three-reader two-track (3R2T) system is studied where two two-dimensional equalizers and a joint detector are used to detect data from two tracks. Analysis shows strong cross-correlation between the noise components at the two equalizers' outputs. Two approaches are presented to handle the cross-correlation in the equalizer and detector, respectively. Simulation results demonstrate that significant performance gain can be achieved using the two proposed approaches.