conscription does not exist
According to the Embassy of Djibouti in Washington DC military service is not compulsory. 
Apparently, joining the armed forces is voluntary.
In 1994 it was reported that the Djibouti government discriminated against citizens on the basis of ethnicity in terms of employment and advancement. The armed forces - as well as the government - mainly consisted of members of the Issa, the dominant Somali clan in Djibouti. 
2 Conscientious objection
There is no known legal provision for conscientious objection.
No information is available about the penalties for disobedience and desertion.
Cases of desertion among regular army soldiers in the Northern part of Djibouti have been reported.  
The forces of the Democratic Front for the Liberation of Djibouti were disbanded in 1983, when Djibouti normalised its relations with Ethiopia. Previously the Front trained armed forces consisting of secondary school students and boys as young as 13. 
Until 1991 the armed forces of Djibouti consisted of volunteers. In 1991 an armed conflict broke out between the government forces and the Front for the Restoration of Unity and Democracy (FRUD), a merger of three opposition groups. FRUD is an Afar-based insurgency movement that alleges discrimination against the Afars by the Issa-led government. Young men and even boys joined the FRUD in great numbers.   
In response to this insurrection, the Djibouti government introduced conscription of all men between 18 and 25 years of age. The armed forces, including national security forces, appear to have more than quadrupled in size between 1991 and 1993, reaching some 20,000 in 1993.  
On 26 December 1994, the government and the FRUD signed a peace and reconciliation agreement. The peace agreement provides for, among other things, the integration of former FRUD combatants into the Djibouti regular armed forces, thus, responding to one of FRUD's demands for 'ethnic parity for Afars and Issas within national security organizations'.  
Apparently, following the peace agreement conscription was abolished.
6 Annual statistics
The armed forces are 9,600 strong, including the 1,200 strong Gendarmerie, but excluding the 3,000 strong National Security Force. The armed forces comprise 1.4 percent of the population. 
 Woods, D.E. 1993. Child Soldiers, the recruitment of children into the armed forces and their participation in hostilities. Quaker Peace and Service, London, UK.  DIRB, 1995. Embassy of the Republic of Djibouti, Washington DC. 4 May 1995. Telephone interview with official.  US State Department 1994. Country Reports on Human Rights Practices for 1993. Washington DC.  US State Department 1995. Country Reports on Human Rights Practices for 1994. Washington DC.  The Indian Ocean Newsletter 1994/1995. 'Djibouti: Ismail Omar Gelleh's Peace.' No. 644, 29 October 1994; 'Djibouti: The Dove of Peace.' No. 653, 7 January 1995; 'Djibouti: Army Integration for FRUD.' No. 655, 21 January 1995. The Indian Ocean Newsletter, Paris.  Africa South of the Sahara 1994. Europa Publications.  'Désertion', in: Le Point, 14 January 1994. Paris, France.  'Murderous Firefights in the North', in: Indian Ocean Newsletter, 5 March 1995. Paris, France.  Institute for Strategic Studies 1997. Military Balance 1997/98. ISS, London, UK.