By Hugh Bronstein

BUENOS AIRES (Reuters) - Argentina's double-digit inflation has shown signs of easing this month, the central bank said on Tuesday as it cut its 35-day reference rate for the eighth week in a row.

As part of its effort to get Latin America's No. 3 economy out of the doldrums while containing consumer prices, the bank sliced 75 basis points off the interest rate to 30.75 percent.

In a statement announcing the cut, the bank cited "a declining tendency in inflation during the month of June."

By lowering the rate and making local bonds less attractive, policymakers hope businesses will direct more cash toward brick-and-mortar investments needed to stimulate growth.

The cuts in the reference rate signal confidence that inflation, estimated by the government at a 40 to 42 percent annual rate in May, is easing.

After Tuesday's reduction the rate was 725 basis points lower than eight weeks ago when the bank started cutting.

President Mauricio Macri took office in December and quickly dismantled heavy economic controls that had been implemented by his predecessor, two-term leader Cristina Fernandez.

An easing of inflation would come as good news to low-income Argentines hit hard by Macri's policies, including reductions in energy and transportation subsidies. Less than a week after assuming office, Macri removed currency controls, allowing for a roughly 30 percent devaluation of the local peso <ARS=RASL>.

The weaker peso increased the cost of imported goods, prodding what was one of the world's highest inflation rates even higher in the first part of this year.

The government will release first-quarter gross domestic product data on Wednesday. Analysts in a Reuters poll said they expect the figures to show a 1.3 percent economic contraction in the first three months of the year.

It will be the first 2016 GDP data release by the Macri administration. He ordered a revamp of the official Indec statistics agency after years of criticism from private economists that it manipulated numbers to make the economy look better than it was under Fernandez, a claim she dismissed.

(Reporting by Hugh Bronstein; Editing by Richard Chang)