Consumers Union yesterday filed suit accusing the Federal Reserve Board of acting "without authority" in abolishing the cooling-off period in which house buyers have three days to back out of certain financing arrangements.

A provision of the 1969 Truth-in-Lending Act, the cooling-off period was designed as a safeguard for consumers who secured credit by putting up their houses as collateral - only to realize late that they could actually lose their houses in the event of a default.

The controversy began in July when the Fed amended its Regulation Z - Truth in Lending - exempting "individual transactions under an open end credit arrangement when the creditor and the seller was not the same or related persons."

Credit cards, and overdraft checking-arrangements frequently found in banks today, were given as examples of open-end credit.

In other words, if a consumer made a large purchase using such an open-ended credit arrangements, and his house was listed as collateral on the credit plan, he would not, under the new provision, have three days to back out.

Consumers Union called the Fed amendment proposal "arbitrary and capricious," and said it would "once again (leave) unwary consumers vulnerable to loss of their homes."

Three weeks ago Sen. William Proxmire (D-Wisc.) and Sen. Donald Riegle (D-Mich.) wrote Fed Chairman William Miller with their concerns over the new provision.

This week, in a response to their letter, Miller wrote back saying, "substantially similar concerns were expressed in a recent letter to the board from staff of the Federal Trade Commission."

Miller said his staff, after checking nearly a year's worth of public comment on the subject, "significantly revised" the proposed changes to limit the exemptions referred to "only to third-party creditors, and not to sellers of goods, in the belief that overextensions was not likely when the seller was not also providing the credit."

Miller also said, "Consideration is being given to a modification in the amendment under which may creditor offering an account of his kind would first be required to file a notification of intent," which would allow the board to monitor the situation for potential abuse.

Until now, Miller contended, "neither the board not the commission staff knows of any instance of abuse arising from the use of second mortgages to secure open-end credit."