Measurements are reported of the coexistence curve and electrical conductivity of the partially miscible aqueous solution of tetra-n-pentylammonium bromide near its consolute point, which was located at Tc = 404.90 ± 0.01 K and approximately 0.03 in mole fraction. The compositions of coexisting phases were measured over three decades of temperature, from 21 to 0.01 K from the consolute point. The conductivity was measured in the supercritical regime, from high dilution to compositions exceeding the critical. The degree of dissociation was estimated to be higher than 20% at the critical composition. In the data analysis, attention was given to the assessment of experimental error and proper weight assignment, and also to asymptotic range and choice of order parameter. No evidence of classical behavior was found. This finding is in contrast to several recent reports of effectively classical critical behavior in ionic solutions similar to ours; but it is in accordance with earlier measurements in very weak electrolytes. We present reasons why our conclusion differs from these recent results; an explanation is given why nonclassical behavior might be expected in systems of this type.