The enquiry began on March 18 and is expected to last three weeks.
It was deemed necessary by the representative appointed by the Scottish government after Dart appealed to it on the grounds of non-decision.
If the CBM development is approved the gas will be delivered into the national grid, while the produced water will be treated to standards agreed with the Scottish Environmental Protection Agency and discharged to the Firth of Forth Rivers under licence.
Over the 20 to 25-year life of the proposed development, the expected gas recuperated will amount to 0.02% of the annual UK gas consumption.
"We are pleased to have the opportunity through the public inquiry of demonstrating the important strategic role gas will need to play in delivering safe, secure and economical energy to the UK in the coming decades as we transition to a low,” Dart Energy UK country manager Douglas Bain told World Coal.
"We will seek through the public inquiry to address and allay with scientific rigour the concerns of the communities and at the same time correct the many myths surrounding the production of coal bed methane."