We compute the parametric correlation function of the conductance peak
s in chaotic and weakly disordered quantum jots in the Coulomb blockad
e regime and demonstrate its universality upon an appropriate scaling
of the parameter. For a symmetric dot we show that this correlation fu
nction is affected by breaking time-reversal symmetry but is independe
nt of the details of the channels in the external leads. We derive a n
ew scaling which depends on the eigenfunctions alone and can be extrac
ted directly from the conductance peak heights. Our results are in exc
ellent agreement with model simulations of a disordered quantum dot.