By overwhelmingly passing a tough fair housing bill, the Senate this week put teeth in federal laws forbidding discrimination against renters and home buyers. Some of it was badly needed, but there is reason to wonder if the law doesn't go too far in some respects.

Fair housing laws already apply in cases of race or gender. The new measure extends protection to the handicapped and families with children. It also provides for government prosecution instead of civil lawsuits, and stiff fines that start at $10,000 for a first conviction.The Senate measure is similar to a House bill passed earlier. The two versions must be ironed out and the Senate bill is expected to prevail. It will then go to President Reagan, who has already praised the legislation.

Major impacts will be immediate. For example:

- Families with children cannot be denied rental housing, except in senior citizen communities. So-called adult complexes will not be able to turn away families with children under age 18. Landlords fearful that children will be too noisy or will tear the apartment to shreds will have to rent to families anyway.

- Handicapped persons may no longer be denied housing. In fact, the law goes much further. It says that handicapped tenants may make improvements in the dwelling at their own expense and do not have to restore the interior to its original condition when they move out.

- Construction of multi-family housing of four or more units intended for occupancy 30 months after the bill becomes law will have to meet expensive new standards for the handicapped. These include such things as lower light and thermostat switches, wider doors, kitchens wide enough for a wheelchair, and brace bars in the bathrooms.

Critics have called the bill a massive and unprecedented federal building code imposed on private sector housing. There is some truth in that. Does this mean the need for federal housing inspectors? In addition, enforcement of the housing law would seem to require thousands of investigators.

Under previous law, a person who has been discriminated against had to file suit as an individual. The new law says such a person may have the government investigate and prosecute. Cases could go either to a jury trial or before an administrative law judge. With an estimated two million cases of housing discrimination last year, investigations alone could require a major bureaucracy.

Fair treatment in renting or buying housing should be encouraged. But the federal government has a way of taking a principle and turning it into a huge and complex program that extends federal power into every little thing - like decreeing how far from the floor light switches must be.

Congress should keep a careful eye on the new law and take steps to curb some of its provisions if it appears the resulting red tape threatens to strangle the rental housing industry while trying to improve it.