  In this paper, we report VLBA radio maps at three frequencies and an ASCA
X-ray spectrum of the water megamaser galaxy NGC 2639, which is believed to
contain an edge-on viewed accretion disk. The radio observations reveal a
compact ($<$ 0.2 pc) nuclear source with a spectrum that turns over sharply
near 5 GHz. The X-ray spectrum shows emission in excess of a power-law model at
energies greater than 4 keV; we interpret this excess as compact, nuclear, hard
X-ray emission with the lower energies photoelectrically absorbed by an
equivalent hydrogen column of $\simeq$ 5 $\times$ 10$^{23}$ cm$^{-2}$.
  If we assume that the turnover in the radio spectrum is caused by free-free
absorption and that both the free-free and photoelectric absorptions are
produced by the same gaseous component, the ratio $\int n_{e}^{2} dl/\int n_{H}
dl$ may be determined. If the masing molecular gas is responsible for both
absorptions, the required ionization fraction is $\gtrsim 1.3 \times 10^{-5}$,
which is comparable to the theoretical upper limit derived by Neufeld, Maloney
& Conger (1994) for X-ray heated molecular gas. The two values may be
reconciled if the molecular gas is very dense -- $n_{H_{2}} \gtrsim 10^{9}$
cm$^{-3}$. The measured ionization fraction is also consistent with the idea
that both absorptions occur in a hot ($\sim$ 6,000K), weakly ionized
(ionization fraction a few times 10$^{-2}$) atomic region that may co-exist
with the warm molecular gas. If this is the case, the absorbing gas is $\sim$ 1
pc from the nucleus. If our line of sight passes through more than one phase,
the atomic gas probably dominates the free-free absorption while the molecular
gas may dominate the photoelectric absorption.
