If you are the sole copyright owner of the musical work, and have not assigned your rights to a music publisher or third party, you do not need to apply for a mechanical license to release the recording in the United States or Canada, only. However, if you plan on releasing this work in any other territory, you are required to get a mechanical license even if you are the sole copyright owner of the musical work being recorded and commercially released. 

If you do not own or administer 100% of the copyright in the song, regardless of where you are planning on releasing it, you are required by law to obtain a mechanical license for the share(s) you don't control. 

If you are looking to release a song outside of the USA, these are the societies that will issue you the proper licenses:

Australia - AMCOS
Austria - AUSTRO-MECHANA
Belgium - SABAM
Brazil - UBC
Canada - CMRRA
France - SACEM
Germany - GEMA
Mexico - SACM
Netherlands - STEMRA
Ireland - MCPS (Ireland)
Italy - SIAE
Japan - JASRAC
Portugal - SPA
Scandinavia - NCB
South Africa - CAPASSO
Spain - SGAE
Switzerland - SUISA
UK - MCPS (part of PRS for Music)

Within the USA you can either contact the publisher directly or go through the Harry Fox Agency (HFA). 

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