Double covering of the Painleve I equation and its singular analysis

In this note, we will do analysis of accessible singular points for a polynomial Hamiltonian system obtained by taking a double covering of the Painleve I equation. We will show that this system passes the Painleve $alpha$-test for all accessible singular points $P_i (i=1,2,3)$. We note its holomorphy condition of the first Painleve system.