MAKE NO MISTAKE about it: home rule in the District of Columbia is alive (if not complete) and well -- and it has been so deemed in terms that the rest of the country should notice and respect. Not only has the law-making ability of a government elected by the residents been tested and upheld by Congress and the White House, but also its qualifications to assume new responsibilities and to manage its finances in a sound fashion have been affirmed on Capitol Hill and Wall Street alike. Wherever there may be doubts or false stereotypes about Washington the Home of Local People, these quite recent developments deserve notice:

A Republican-controlled Senate, a Democratic- majority House and the Reagan administration -- having thoroughly reviewed proposals to tighten federal control over certain local law-making powers -- agreed that this wasn't necessary, that, on the contrary, the process could be made more uniform and be left more to local discretion without weakening any general federal responsibility.

In turn, these same branches of the federal government freed the District to issue bonds and notes authorized by the local government.

The D.C. government has received the highest ratings possible from Moody's Investors Service and Standard & Poor's -- the country's foremost municipal-finance rating services -- for short-term borrowing. This indicates that the District government has a strong system of cash flow and reserves -- and enables the local government to pay the lowest possible interest rate for short-term loans.

Congress and the White House have approved a record 1985 federal payment to the District (in lieu of local revenues that would be raised if land used by the federal government were taxed).

The administration and Congress have worked out the long-awaited transfer of St. Elizabeths Hospital from the federal government to the District.

To other Americans whose local governments make laws, borrow money, issue bonds and perform all sorts of other functions as a matter of muncipal course, these new responsibilities may seem routine and a matter of right. They should be -- which is all that people here are saying in their search for new understanding and assistance in the 50 states where ratification of the D.C. congressional representation amendment needs urgent approval.