We report the results of the analysis of new ASCA observations and archival ROSAT data of the compact luminous X-ray source found at the edge of the nearby star-forming dwarf galaxy ( catalog Holmberg II ) ( ( catalog UGC 4305 ) ) in the ( catalog M81 ) group . We have found a number of new features in the X-ray properties of this source . Our new ASCA spectrum revealed that the X-ray emission extends to the hard band and can be best described by a power-law with a photon spectral index \Gamma \sim 1.9 while a kT \sim 5 [ keV ] thermal plasma with a low abundance ( \sim 0.2 Z _ { \sun } ) is also acceptable . The ASCA spectrum does not fit with a multi-color disk blackbody , unlike some off-nucleus X-ray sources with similar luminosities . The joint ASCA - ROSAT spectrum suggests two components to the spectrum : the hard power-law component and a warm thermal plasma ( kT \sim 0.3 [ keV ] ) . An additional absorption over that of our galaxy is required . The wobble correction of the ROSAT HRI image has clearly unveiled the existence of an extended component which amounts to 27 \pm 5 \% of the total X-ray emission . These observations indicate that there are more than one component in the X-ray emission . The properties of the point-like component is indicative of an accretion onto an intermediate mass blackhole , unless a beaming is taking place . We argue that the extended component does not come from electron scattering and/or reflection by scattered optically-thick clouds of the central radiation . Possible explanations of this X-ray source include multiple supernova remnants feeding an intermediate-mass blackhole .