A connector that is only connected to one shape cannot be imported via JSON.
Tested here:
http://demos.telerik.com/aspnet-ajax/diagram/examples/saveload/defaultcs.aspx

JSON:
{
    "shapes": [{
        "id": "nadal_winner",
        "background": "#f18100",
        "hover": {
            "opacity": 0.2
        },
        "cursor": "pointer",
        "content": {
            "align": "center middle",
            "text": "R. Nadal",
            "color": "#fff"
        },
        "selectable": true,
        "serializable": true,
        "enable": true,
        "type": "rectangle",
        "path": "",
        "visual": null,
        "x": 180,
        "y": 155,
        "minWidth": 20,
        "minHeight": 20,
        "width": 140,
        "height": 30,
        "connectors": [{
            "name": "Top",
            "description": "Top Connector"
        }, {
            "name": "Right",
            "description": "Right Connector"
        }, {
            "name": "Bottom",
            "description": "Bottom Connector"
        }, {
            "name": "Left",
            "Description": "Left Connector"
        }, {
            "name": "Auto",
            "Description": "Auto Connector"
        }],
        "rotation": {
            "angle": 0
        },
        "stroke": {
            "width": 0,
            "color": "#fff"
        },
        "connectorDefaults": {
            "background": "#444444",
            "stroke": {
                "color": "white"
            },
            "hover": {
                "background": "white",
                "stroke": {
                    "color": "#444444"
                }
            }
        },
        "undoable": false
    }],
    "connections": [{
        "from": {
            "shapeId": "nadal_winner",
            "connector": "Right"
        },
        "to": "OK6oDroWug",
        "id": "OK6oDroWug",
        "background": "Green",
        "hover": {
            "stroke": {}
        },
        "cursor": "pointer",
        "content": {
            "align": "center middle",
            "text": "",
            "color": "#444444"
        },
        "selectable": true,
        "serializable": true,
        "enable": true,
        "startCap": "none",
        "endCap": "none",
        "points": [],
        "stroke": {
            "width": 2,
            "color": "#6c6c6c"
        },
        "select": {
            "handles": {
                "width": 8,
                "height": 8,
                "background": "white",
                "stroke": {
                    "color": "#444444"
                }
            }
        }
    }]
}