find the connected covering space of $\mathbb{R}P^2 \lor \mathbb{R}P^2$

find the connected covering space of $\mathbb{R}P^2 \lor \mathbb{R}P^2$

This is a problem on Hatcher' book. How to find all the connected covering
spaces of $\mathbb{R}P^2 \lor \mathbb{R}P^2$? I don't know where to start.
Is there a general way to construct the connected covering space of a
giving space?