Connected sums of 4-manifolds

We study the following problem for closed connected oriented manifolds M of dimension 4. Let Λ=Z[π1(M)] be the integral group ring of the fundamental group π1(M). Suppose G⊂H2(M;Λ) is a free Λ-submodule. When do there exist closed connected 4-manifolds P and M′ such that M is homotopy equivalent to the connected sum P # M′, where π1(P)≅π1(M), π1(M′)≅0, and H2(M′;Z)⊗ZΛ≅G. An answer is given in terms of π1(M) and the intersection forms on H2(M;Λ) and H2(M;Z).