We present a deep X-ray observation of the low-luminosity active galactic nucleus in NGC 4258 ( M 106 ) using the Advanced Satellite for Cosmology and Astrophysics ( ASCA ) . Confirming previous results , we find that the X-ray spectrum of this source possesses several components . The soft X-ray spectrum ( < 2 { \thinspace keV } ) is dominated by thermal emission from optically-thin plasma with kT \sim 0.5 { \thinspace keV } . The hard X-ray emission is clearly due to a power-law component with photon index \Gamma \approx 1.8 absorbed by a column density of N _ { H } \approx 8 \times 10 ^ { 22 } \hbox { $ { \thinspace cm } ^ { -2 } $ } . The power-law is readily identified with primary X-ray emission from the AGN central engine . Underlying both of these spectral components is an additional continuum which is possibly due to thermal emission of a very hot gaseous component in the anomalous arms and/or the integrated hard emission of X-ray binaries in the host galaxy . We also clearly detect a narrow iron K \alpha emission line at \sim 6.4 { \thinspace keV } . No broad component is detected . We suggest that the bulk of this narrow line comes from the accretion disk and , furthermore , that the power-law X-ray source which excites this line emission ( which is typically identified with a disk corona ) must be at least \sim 100 GM / c ^ { 2 } in extent . This is in stark contrast to many higher-luminosity Seyfert galaxies which display a broad iron line indicating a small ( \sim 10 GM / c ^ { 2 } ) X-ray emitting region . It must be stressed that this study constrains the size of the X-ray emitting corona rather than the presence/absence of a radiatively efficient accretion disk in the innermost regions . If , instead , a substantial fraction of the observed narrow line originates from material not associated with the accretion disk , limits can be placed on the parameter space of possible allowed relativistically broad iron lines . We include a discussion of various aspects of iron line limb-darkening for highly inclined sources , including the effect of gravitational light-bending on the apparent limb-darkening law . By comparing our data with previous ASCA observations , we find marginal evidence for a change in absorbing column density through to the central engine , and good evidence for a change in the AGN flux . We conclude with a brief discussion of two serendipitous sources in our field of view ; the QSO Q1218+472 and a putative z \sim 0.3 cluster of galaxies .