The decline followed an 8 percent increase in October and a 6.7 percent drop in November, the data agency said.
The value of construction intentions in December came to $6.85 billion with the decline paced by lower construction intentions for multifamily residential and commercial projects in British Columbia and Ontario, StatsCan said.
For 2013, the value of projects granted building permits came to $80.8 billion, off 0.1 percent from 2012.
Residential construction permits granted in December fell 9.3 percent to $3.7 billion, falling for the second consecutive month.
Quebec and New Brunswick posted gains residential projects in December, the only two provinces to do so.
In commercial building, the value of projects for which permits were issued rose 3.7 percent to $2.8 billion following a 4.5 percent decline in November.
Commercial permits by value fell in Saskatchewan and Manitoba and, to a lesser extent, four other provinces. Gains in commercial construction permits were posted by Alberta, Quebec and Newfoundland and Labrador. All other provinces posted declines, StatsCan said.