After 13 years of planning and discussion, a new Montgomery County courthouse and government office complex took two key steps toward reality last week.

The Rockville mayor and city council formalty approved the sale to the county of the 5.1 acres of land where the complex will be built. The county returned the favor with a check for $2,560,500.

It covers the cost of the 5.1 acres, as well as leasing rights to 270 nearby city-owned parking spaces.

Construction of the two new buildings is thus free to begin in April. It is expected to be finished in late 1981. A contractor is scheduled to be chosen by the end of January. The project will cost more than $30 million and will be, by far, the largest single piece of construction the county, has ever undertaken.

Officially named the County Government Center, the new complex will consist of two towers.

The larger 18 stories high, will house all 1,730 office employees of the county's headquarters in 272,924 square feet.

More than 1,000 of those employees now work in leased offices scattered from Silver Spring to Germantown.

The smaller tower, 10 stories high, will be the new home of the county's circuit court. It will provide 14 new, circular courtrooms and 313,217 total square feet of space.

In a ground-level mall just west of the office tower will be an outdoor ice skating rink.

The Government Center will be built on a rectangular plot just south of Rockville Mall and just west of Rockville Pike in downtown Rockville. It will be bounded by East Jefferson Street on the south, the old courthouse on the west, Rockville Mall on the north and a housing project for the elderly called Town Center Apartments on the east. The site is now a grassy field.

The present county office building built in 1955 and expanded twice, will continue to be used by the county council and for computer operation.

The present courthouse, with one section dating to 1938, will become the new, centralized home of the county's district courts, which now are headquartered on Shady Grove Road farther north in Rockville.

The Government Center is being financed by a $42-million , 25-year bond. But county offficals pointed out that Montgomery taxpayers will actually save $115 million over the life of the bond.

The reason is the 35,000 square feet of office space that the county now leases, at a cost of more than $1.8 million a year. More than 200,000 of those square feet will be abandoned by the county as soon as the Government Center is finished.

"A lot of people made a big deal out of the $42 million over the years," said A.S. (Migs) Damiani, deputy director of the county's office of community and economic development. "But I really can't understand what the boondoggle is.

"We're saving a lot of money . . .. There's no question the county should have made this decision years ago."

The new complex will contain all the latest in building design - indirect lighting, energy-conscious heating and windows, even a system that can conduct electronic weapons surveillance of anyone approaching a judge's chambers.

But the complex will deliberately provide too few parking spaces.

There will be 505 new spaces built below the new office tower. And employees will be able to use 270 leased spaces, and 200 more rented ones, in nearby Rockville Mall. Still, by Damiani's estimate, that will leave the complex 400 spaces short of what present car-to-employee ratios call for.

"We're depending that people will be car-pooling more and relying more on Public transportation," Damiani said. "We have to comply with air quality standards of the future."

Damiani pointed out that Metro's Shady Grove line is expected to open at the same time as the new office complex. A stop will be two blocks away. In addition, he said, the county retains the option of adding to an existing three-story parking garage just south of the Center.

The parking spaces the county will lease and rent at Rockville Mall will be only part of the increased activity Rockville officials hope to see there.

Rockville city manager Larry N. Blick said he anticipates an additional $800,000 a year in mall sales, mostly in lunches, once the Government Center opens. The seven-year-old Mall has been plagued by poor volume and high crime since it opened.

As part of its land-sale agreement with Rockville, Montgomery County agreed to construct an extra lane of highway on the north side of Jefferson Street, between Maryland Avenue and South Washington Street. Jefferson Street (Rte. 28) is the main access route from downtown Rockville to Interstate 270. Contruction of the extra lane is expected to begin in 1979.