Ask Mr. Smarty Plants

You can visit the Recommended Connecticut page to see a list of plants native to Connecticut that are commercially available for landscaping. You can use the NARROW YOUR SEARCH option to select by General Appearance, Light Requirement, Soil Moisture, etc.  From that list (and elsewhere) I found several plants that should work well as a groundcover depending on the light conditions of your slope. 

Sun = 6 or more hours of sun per day, Part shade = 2 to 6 hours of sun per day, Shade = less than 2 hours of sun per day

Sibbaldiopsis tridentata (Shrubby fivefingers)—sun in gravelly soils

Arctostaphylos uva-ursi (Kinnikinnick)—sun, part shade and shade in rocky or sandy soils, evergreen

Dryopteris marginalis (Marginal woodfern)—part shade and shade in rocky soil, evergreen

Gaultheria procumbens (Checkerberry)—part shade and shade in variable soils, evergreen

Maianthemum stellatum (Starry false lily of the valley)—part shade and shade and likes sandy soils

Mitchella repens (Partridgeberry)—part shade and shade and will grow in sandy soils, evergreen

Phlox pilosa (Downy phlox)—sun and part shade in sandy or rocky soil

Juniperus horizontalis (Creeping juniper)—sun and part shade in dry rocky soils, evergreen.  Here are photos and more information.

You can see more possibilites on the Connecticut Botanical Society webpage.

Grasses make good taller groundcovers that are excellent for erosion control because of their extensive fibrous root systems that hold the soil in place.   Here are a few suggestions for native Connecticut grasses:

Andropogon virginicus (Broomsedge bluestem)—part shade and will grow in dry, sandy soils

Bromus kalmii (Arctic brome)—sun and grows in sandy soil and rocky banks

Carex blanda (Eastern woodland sedge)—sun, part shade and evergreen

Schizachyrium scoparium (Little bluestem)—sun and part shade in sandy soils