The Branch House is set on a slight hill on an open site. In plan, the one-story house is square with a two-story, gable-and-hipped-roofed light monitor at the center of the square. A square-plan garage wing is attached to the north end of the house; a swimming pool with a flagstone patio is at the south end. The main entrance is sheltered under a gable-roofed porch with square columns; this entrance originally was covered by a wood pergola.
As with many of his houses from this time period, Christ-Janer experimented with different roof planes and angles in the Branch House. The Branch House features his typical right-angle dormers (essentially shed-roofed dormers turned at a 90-degree angle so that the dormer windows face the gable end of the building, reminiscent of a sawtooth roof); this design device is also used at the Grant House (1981) across the street and the Ackerman House (1975). Originally, most of the Grant House windows on the west and east facades were designed to be angled bay windows with glazing at only the south-facing side of the bays, but these have been removed and replaced with windows flush with the wall plane.
The Branch House does not have expansive areas of glass except at the south facade, which has three levels of fenestration: sliding glass doors at the basement and first-floor levels, and fixed and horizontal sliding sash in the right-angle dormers. Wood decks and stairs lead from the first floor to the swimming pool at the south end of the house.
The Branch House was designed by Victor Christ-Janer in 1978 for David S. and Elizabeth T. Branch. Although the assessor field cards indicate that the Branches purchased the lot from Arthur W. Hooper, Jr., Trustee, in 1979, Elizabeth Branch stated that they acquired the land from Christ-Janer for $120,000 in 1978, a price that included his architectural design fee. Christ-Janer owned a 24-acre parcel and intended to divide the land into five building lots with the remaining land going to the New Canaan Land Trust (instead eventually transferred to the Audubon Society). Christ-Janer put in a new road and designed at least three houses in the development, including the Grant House (1981) located across the street from the Branch House.
According to Elizabeth Branch, Christ-Janer designed the Branch House to use "passive solar energy" to address the energy crisis of the late 1970s in the United States. He did not place any windows on the north side of the building and shielded the windows on the east and west by creating angled bay windows with sash that faced south, a design he called "horse-blinder windows." The majority of the fenestration on the building was on the south facade, and three solar panels facing south fed a hot water system (later removed because of roof leakage). On the interior, Christ-Janer used ceramic floor tiles and a stone wall to retain heat. A two-story atrium (expressed as a gable-and-hipped-roofed light monitor on the exterior) contained a fan to circulate warm air throughout the house. The basement level was set below ground level to keep it cool in the summer.
The Branch House was constructed between 1979 and 1980 by Landworks Associates, Inc., a Southport, Connecticut-based company recommended by Christ-Janer because he had taught one of its principals, Roger P. Ferris, at the Columbia University School of Architecture. The construction cost was $255,000. A swimming pool was constructed on the site between 1984 and 1985. The Branches also finished the basement as a suite for their teenage child at an unknown date.
Eric L. Straus purchased the property in 2004. Eric and Adriane Straus altered the front porch by removing the pergola and replacing it with a gable-roofed porch. They also removed the angled bay windows (i.e., "horse blinder windows"), replacing them with windows set flush with the exterior walls, and painted the exterior siding, which had originally been stained grey. The kitchen and bathrooms were also upgraded.