  We compute the parametric correlation function of the conductance peaks in
chaotic and weakly disordered quantum dots in the Coulomb blockade regime and
demonstrate its universality upon an appropriate scaling of the parameter. For
a symmetric dot we show that this correlation function is affected by breaking
time-reversal symmetry but is independent of the details of the channels in the
external leads. We derive a new scaling which depends on the eigenfunctions
alone and can be extracted directly from the conductance peak heights. Our
results are in excellent agreement with model simulations of a disordered
quantum dot.
