  The Katz-Sarnak Density Conjecture states that the behavior of zeros of a
family of $L$-functions near the central point (as the conductors tend to zero)
agree with the behavior of eigenvalues near 1 of a classical compact group (as
the matrix size tends to infinity). Using the Petersson formula, Iwaniec, Luo
and Sarnak \cite{ILS} proved that the behavior of zeros near the central point
of holomorphic cusp forms agree with the behavior of eigenvalues of orthogonal
matrices for suitably restricted test functions. We prove a similar result for
level 1 cuspidal Maass forms, the other natural family of ${\rm GL}_2$
$L$-functions. We use the explicit formula to relate sums of our test function
at scaled zeros to sums of the Fourier transform at the primes weighted by the
$L$-function coefficients, and then use the Kuznetsov trace formula to average
the Fourier coefficients over the family. There are numerous technical
obstructions in handling the terms in the trace formula, which are surmounted
through the use of smooth weight functions for the Maass eigenvalues and
results on Kloosterman sums and Bessel and hyperbolic functions.
