Surviving church registers for Colne (if not at the church or chapel) have typically been deposited at Lancashire Archives. Some have been transcribed and/or indexed, and full details of what is available can be found in the guides here for all denominations.
Most Anglican church registers – Holy Trinity, St Batholomew’s and Christ Church – are also available search online at ancestry.co.co.uk (free in Lancashire Libraries and Lancashire Archives) and transcriptions can be found for free, online, courtesy of Online Parish Clerk.
The archive collections for the churches and chapels in the town are kept at Lancashire Archives and contain a huge amount of information about the history of religion in the town. The archive catalogues can be browsed online:
Other material relating to organised religion in the town can be found in numerous other collections too, so it is worth doing some keyword searching across all collections in the Lancashire Archives online catalogue.