In this paper a constrained relative attitude determination solution of a formation of two vehicles is considered and the effect of constraint violation on the estimation error is studied. The solution for the relative attitude between the two vehicles is obtained only using line-of-sight measurements between them and a common (unknown) object observed by both vehicles. The solution represents the minimum number of measurements required to determine the relative attitude and no ambiguities are present. The constraint used in the solution is a triangle constraint on the vector observations. This constraint represents an ideal situation, which may be violated in practice due to sensor misalignments and/or noisy measurements. A sensitivity analysis is performed in order to assess how out-of-plane observations affect the overall solution. In particular, an analytical expression for this sensitivity is derived. Simulations runs are also shown to verify the analytical expression.