A little late to the party on this one, however the accepted answer by @Narenda didn't completely solve my problem. This may help someone else that stumbles across this later.
If you need a single select only, here's a way of doing it:
Extend the jsGrid plugin with a method to find a row by index:
    jsGrid.Grid.prototype.rowByIndex = function(arg){
        //this._content.find("tr")[arg] returns a DOM element instead of a jQuery object
        //Pass the DOM element to the find method to get a jQuery object representing it
        return this._content.find(this._content.find("tr")[arg]);
    };
Modify the rowClick function in @Narenda's answer:
    rowClick: function ( args ) {
        //Deselect all rows
        for(var i = 0; i<this.data.length; i++){
            this.rowByIndex(i).removeClass("jsgrid-highlight-row");
        }
        //Everything else as per the previous answer
        var $row = this.rowByItem(args.item),
        selectedRow = $("#jsGrid").find('table tr.jsgrid-highlight-row');
        if (selectedRow.length) {
            selectedRow.toggleClass('jsgrid-highlight-row');
        };
        $row.toggleClass("jsgrid-highlight-row");
        //Any other code to run on item click
    }
And add some CSS. This mimics the row hover in the default theme:
    tr.jsgrid-highlight-row td.jsgrid-cell {
         background:#c4e2ff;
         border-color:#c4e2ff;
    }