Justice is set in motion following the commission and report of an offence to the police targeting to initiation of crime investigation (CPC, 1961). Ethiopian laws do not locate when the investigation shall start. Though laws are silent, police officers may start inquiry at any time to set justice in motion in practice. After justice is set in motion through channels of crime reporting (CPC, 1961, Articles 11, 12 & 19), the question of frequency and duration of investigation is under quandary since it is treated by different legislations differently. The 1961 Ethiopian criminal procedure code was the first document which dealt with the frequency and duration of investigation for the first time in Ethiopian criminal justice history. The FDRE constitution is the other document which locates the concept of duration of investigation at higher level. The Ethiopian criminal policy document envisaged different frequency and duration of crime investigation to be provided by law depending on the complexity and nature of the offence (FDRE Criminal Justice Policy, 2011). After the coming forth of this policy document, different legislations are enacted. The vagrancy control proclamation, the anti-terrorism proclamation, the new draft criminal procedure and evidence law are among the laws. These laws have intricacy concerning constitutionality, consistency and merit. Thus, the writer investigated these issues and analyzed the legislations with regard to the objectives of criminal justice policy.