It is well known that if $X$ is a $1$-connected (i.e. path connected and simply connected) 2-dimensional finite simplicial complex, then $X$ is homotopy equivalent to a wedge of $2$-spheres.
Consider the more general setting where $X$ is path connected, and $\pi_1(X)$ is a free group. Is this enough to imply that $X$ is homotopy equivalent to a wedge of $1$-spheres and $2$-spheres?
I think the answer is yes: if $X$ is a connected finite 2-dimensional CW-complex with $\pi_1(X)$ free, then $X$ is homotopy equivalent to a wedge of 1-spheres and 2-spheres. This is stated in the paragraph spanning the first and second pages of Trees of Homotopy Types of Two-Dimensional CW-Complexes by Dyer and Sieradski, available here: http://link.springer.com/article/10.1007%2FBF02566109
