It rejected by 20 votes to 19 a move by the Leader of the opposition, Sir Charles Court, to disagree with a ruling by the Speaker, Mr Norton.
The Bill seeks to repeal the ban on scientology enacted by the Liberal-Country Party Government in 1968.
Mr Norton ruled that the Bill was not subjudice because of a writ by the Church of the New Faith Incorporated against the director of the Mental Health Services, Dr A.S. Ellis.
The church is claiming damages against Dr Ellis for a libel allegedly contained in a report dated February 15 this year.
Sir Charles said that the writ was based entirely on the February 15 report to which the Opposition would have to refer to debate the Bill properly.
"I submit that it is impossible for this side to debate this Bill without impinging on this report," he said.
"This man, Dr Ellis, is one of the foremost authorities in our State on this particular issue. No man has had more experience in this particular subject than he has and the whole climax of his report is in the last paragraph in which he expresses an opinion."
The Premier, Mr Tonkin, said that Parliament had a right to introduce legislation to amend any law.
No action in a court, either in course or pending, could take away Parliament's inherent right to amend the law.
Parliament's right to legislate in all circumstances remained supreme.
Mr R. Hutchinson (Lib., Cottesloe) told the Legislative Assembly that a resurgence of scientology would not be in the best interests of the community.
He said that the damage to people's lives caused by scientology was a fact of life.
Mr Hutchinson, a former Minister for Health, said that although the Church of the New Faith had removed many of scientology's practices, it could easily reinstate them if the ban on scientology was lifted.
Dr Ellis's report, which has been tabled in the Legislative Assembly, ended: "I am of the opinion that the evidence collected and produced indicates that scientology is indeed a danger to public health and as such I believe that it would be very much against the public interest if the present Act were repealed."
Mr Hutchinson quoted a letter he had received from the Rev. Michael Graham, the president of the Church of the New Faith. The letter said that there was no need to ban a device called the E-meter because of the monopoly that scientologists had on it.
The letter said: "There has never been any doubt that the E-meter works.
"The church has made the following unprecedented offer:
"Why try to suppress an area of technology? It is a powerful tool with secular application in the hands of the trained individual."
Mr Hutchinson said that the letter defied description.
The debate was adjourned.
Later, the Minister for Health, Mr Davies, said that there were no practising qualified psychiatrists or psychologists in his department on record as favouring the repeal of the Scientology Act.