A congressional consultant charged yesterday that President Carter's nominee to the Federal Election Commission took improper deductions and made a miscalculation that saved him at least $13,000 in income tax during several recent years.

Asked if what the nominee, John McGarry, had done was illegal, the consultant. Reka Hoff of the General Accounting Office, said she believed it was, but stressed that she needed more information to tell exactly what errors McGarry might have made.

After McGarry agreed to authorize the Internal Revenue Service to release files showing exactly what areas of his tax returns had been audited, the hearing before the Senate Rules Committee was recessed to allow Hoff and the committee staff to study the IRS files.

The confirmation hearing may be resumed today. A committee vote McGarry's nomination is scheduled for tomorrow.

The tax charges - and questions about the thoroughness of IRS audits of McGarry - have confused the already long-delayed Senate consideration of the nomination.

McGarry, a special counsel to the House Administration Committee and a friend of House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) was selected by Carter for a Democratic seat on the politically sensitive FEC.

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Committee Republicans say they want the questions raised by Hoff's report answered before they vote the nomination.

"This is not a question of how many votes there are," Sen. Mark Hatfield (R-Ore.) said yesterday.

McGarry's nomination was originally linked with the nomination of Sam Zagoria, a former member of the National Labor Relations Board, for Republican FEC seat.

Zagoria's name was withdrawn by the White House two weeks ago, after Republicans protested that he had been chosen without consultation with the party's leaders.

As part of the agreement to withdraw Zagoria, Senate Republicans promised not to prolong McGarry's hearing unnecessarily. But the Republicans, represented by Senate Minority Leader Howard H. Baker, Jr., (R-Tenn.), insisted they would not approve McGarry until he had answered to questions about his extensivce business transactions.

"My natural response would be vote affirmatively for your nomination." Hatfield told McGarry yesterday. "I have always felt the president should be able to pick his own team."

But Hatfield insisted he wants to get answers he feels McGarry has not yet given.

McGarry has upset some committee staff members investigating his background because of what the staff members consider his evasiveness.

At yesterday's hearing, Hoff cited three transactions where she felt McGarry's tax returns were inaccurate or incomplete.

In 1973, McGarry included $35,554 received from an investment in Kenmore Management Co. when computing his self-employment income tax. By including it as self-employment income rather than investment income (as he had done with money from the same firm in 1972), McGarry saved $911, according to Hoff.

McGarry referred the question to his tax counsel, James Linnehan of Boston, who declined to answer, saying the return had been prepared by someone else.

Hoff questioned McGarry's deduction of $26,211 in commuting expenses for the years 1974 through 1976, when he lived in Boston but worked full-time in Washington.

McGarry said that he continued to live in Boston and took the commuting expenses because it was never certain how long the Washington job, assisting the House committee on elections, would last.

Hoff said the laws were clear that commuting expenses could not be deducted.

In documents prepared for the committee staff.Hoff estimated that the deductions for commuting saved McGarry at least $5,900.

A third transaction questioned by Hoff related to a computer leasing arrangement on which McGarry claimed a $67,000 deduction for depreciation in 1974. Hoff said that only a $22,000 deduction was proper, resulting in an increased tax liability of at least $6,300.

McGarry presented a lawyer who handled the transaction, Steve Eastham, who said the deduction was proper. The issue was not resolved.