Step 1: The question tests where the world's first fingerprint bureau came into existence. Although early pioneers like William Herschel and Francis Galton worked in other parts of the world, the institutional bureau itself was first set up in Calcutta.
Step 2: This Calcutta bureau, housed in the Writers' Building, places India as the birthplace of the first dedicated fingerprint identification office.
Step 3: Fingerprinting holds top rank among identification methods because ridge patterns are permanent and individually unique; dental records rank second.
Step 4: Thus England, China, and Singapore can be ruled out.
\[\boxed{\text{India}}\]