Colocated multiple-input multiple-output (MIMO) technology has been widely used in automotive radars as it provides accurate angular estimation of the objects with relatively small number of transmitting and receiving antennas. Since the Direction Of Departure (DOD) and the Direction Of Arrival (DOA) of line-of-sight targets coincide, MIMO signal processing allows forming a larger virtual array for angle finding. However, multiple paths impinging the receiver is a major limiting factor, in that radar signals may bounce off obstacles, creating echoes for which the DOD does not equal the DOA. Thus, in complex scenarios with multiple scatterers, the direct paths of the intended targets may be corrupted by indirect paths from other objects, which leads to inaccurate angle estimation or ghost targets. In this paper, we focus on detecting the presence of ghosts due to multipath by regarding it as the problem of deciding between a composite hypothesis, H0 say, that the observations only contain an unknown number of direct paths sharing the same (unknown) DOD's and DOA's, and a composite alternative, H1 say, that the observations also contain an unknown number of indirect paths, for which DOD's and DOA's do not coincide. We exploit the Generalized Likelihood Ratio Test (GLRT) philosophy to determine the detector structure, wherein the unknown parameters are replaced by carefully designed estimators. The angles of both the active direct paths and of the multi-paths are indeed estimated through a sparsity-enforced Compressed Sensing (CS) approach with Levenberg-Marquardt (LM) optimization to estimate the angular parameters in the continuous domain. An extensive performance analysis is finally offered in order to validate the proposed solution.