Postmaster General Anthony M. Frank yesterday objected to a Democratic proposal that would place dollar limits for the first time on how much official mail each House member and senator could send because it would "assign to the Postal Service {the} policing function."

"Our preferred alternative" for placing limits on so-called franked mailings, Frank said in a letter to Rep. William D. Ford (D-Mich.), "would be to have Congress use the methods of direct accountability, official mail meters, stamps and permit imprints, now used by many other government agencies."

Ford, chairman of the House Committee on Post Office and Civil Service and a strong opponent of any limits on congressional franking, believes Frank's letter "bolsters his arguments that the proposed changes would be expensive and unworkable," according to a spokesman.

Rep. Vic Fazio (D-Calif.), chairman of the House Appropriations subcommittee on the legislative branch, who drew up the initial plan to curb use of the frank, has already taken some of the postmaster general's criticisms into consideration in his most recent drafts of the proposal, according to congressional sources.

Because of objections to the plan from a number of colleagues and the rush of House business, Fazio postponed yesterday's scheduled markup of the fiscal 1991 House appropriation until next Tuesday, sources said.

The increased use of franked mail, particularly by House members in election years, has become an embarrassment to some members and a campaign issue in some races because the cost this election year may exceed the record $77 million spent in 1988, the last election year.

While the Senate instituted individual reporting of mail costs in 1985 and limits last year, the House has taken neither step. This year, its mailings are expected to exceed the $40 million appropriated for that purpose by more than $38 million, according to a recent Postal Service estimate.

Fazio, who must maneuver to get the House's own money bill through Congress, drew up an initial proposal that required the Postal Service to inform any House or Senate member who reached 90 percent of the individual mailing allocation and refuse to carry or deliver any mail once the limit was reached.