The action, started in 1978, came on for hearing before Mr Justice Matheson. He reserved his decision.
In the 17-point claim, the church, and four members representing about 30 other members, is seeking an injunction to:
The injunction also seeks a declaration that the collecting and recording of information relating to the plaintiffs is unlawful and not authorised by the provisions of the Police Regulation Act or any other law.
It further seeks costs against Mr Draper and the State of SA.
The claim says the Church of the New Faith became the Church of Scientology Inc. on March 3, 1975.
As well as the church, the claim lists four plaintiffs: Andrew Symes, John Sowery, Dianna Payne and Doreen Joyce Tuly.
It says the church "has been and has conducted itself as a religious body (and) has sought to advance the spiritual and general welfare of its members and members of the community generally in the State of SA.
"Since a date prior to 1978, but not known to the plaintiffs, (Mr. Draper) has from time to time collected, collated and recorded information relating to (the church) and its members and adherents ..," the claim says.
The information has been recorded in files collected by "certain members of the SA Police Force known as Special Branch."
Despite many requests since 1978 permission to inspect that information had been refused.
The claim says the information does not relate to any criminal or unlawful conduct, either actual or likely.
It claims that it is beyond the power of Mr. Draper and the State of SA to authorise the collecting and keeping of the files and that the collecting and keeping of them is not authorised or empowered by the provisions of the Police Regulation Act or any other law.
The church claims the collecting and keeping of the files have wrongfully interfered with its exercise of its rights to freedom of practice of religion and freedom of expression and congregation.
The claim says the church and its members fear the information may be "false, misleading, inaccurate, defamatory or malicious ... and (its) collection or keeping or communication to other persons may cause the plaintiffs or some of them loss and harm."
It says Mr. Draper "threatens and intends unless restrained to permit, if he sees fit, the communication of the contents of such records and files and information to persons other than the plaintiffs without permission of the plaintiffs."
Mr. J. J. Doyle appeared for the Church of Scientology and Symes, Sowery, Payne and Tuly; the Solicitor-General, Mr. M. F. Gray, with Mr. M. I. Bell for Mr. Draper, the Police Department and the State of SA.