We estimated the dynamical surface mass density (S) at the solar Galactocentric distance between 2 and 4 kpc from the Galactic plane, as inferred from the observed kinematics of the thick disk. We find S(z = 2 kpc) = 57.6 +/- 5.8 M-circle dot pc(-2), and it shows only a tiny increase in the z range considered by our investigation. We compared our results with the expectations for the visible mass, adopting the most recent estimates in the literature for contributions of the Galactic stellar disk and interstellar medium, and proposed models of the dark matter distribution. Our results match the expectation for the visible mass alone, never differing from it by more than 0.8 M-circle dot pc-2 at any z, and thus we find little evidence for any dark component. We assume that the dark halo could be undetectable with our method, but the dark disk, recently proposed as a natural expectation of the Lambda CDM models, should be detected. Given the good agreement with the visible mass alone, models including a dark disk are less likely, but within errors its existence cannot be excluded. In any case, these results put constraints on its properties: thinner models (scale height lower than 4 kpc) reconcile better with our results and, for any scale height, the lower-density models are preferred. We believe that successfully predicting the stellar thick disk properties and a dark disk in agreement with our observations could be a challenging theoretical task.