This work presents a non-linear mathematical model to study the transmission dynamics of ‘Human Immunodeficiency Virus (HIV)’ and ‘Tubercle Bacillus (TB)’ co-infection incorporating the effect of screening of both the HIV and TB infected individuals. The basic reproduction numbers corresponding to both the HIV and TB are obtained and it is shown that the disease free equilibrium is stable only when both the reproduction numbers are less than one. The existence and stability of TB-only and HIV-only equilibria are discussed in-detail. In this work, we observe that the co-infection equilibrium point exists only under some restrictions on the parameters provided both the basic reproduction numbers are greater than one. Importantly, this equilibrium is always unstable. A numerical simulation is reported to support and strengthen the major analytical findings. Furthermore, the effects of screening of the infectives on the equilibrium level of HIV and TB infected population are investigated and it is found that the screening with proper counseling results in a significant reduction in the number of HIV and TB infected individuals.