We consider a static team problem in which agents observe correlated Gaussian observations and seek to minimize a quadratic cost. It is assumed that the observations can be split into two parts: common observations that are observed by all agents and local observations that are observed by individual agents. It is shown that the optimal strategies are affine and the corresponding gains can be determined by solving appropriate systems of linear equations. Two structures of optimal strategies are identified. The first may be viewed as a common-information based solution; the second may be viewed as a hierarchical control based solution. A decentralized estimation example is presented to illustrate the results.