Index: src/wp-admin/js/customize-controls.js
===================================================================
--- src/wp-admin/js/customize-controls.js	(revision 36536)
+++ src/wp-admin/js/customize-controls.js	(working copy)
@@ -2331,6 +2331,10 @@
 				api.HeaderTool.UploadsList,
 				api.HeaderTool.DefaultsList
 			]);
+
+			//Add extra params to doCrop args for customizer
+			wp.media.controller.Cropper.prototype.defaults.doCropArgs.wp_customize = 'on';
+			wp.media.controller.Cropper.prototype.defaults.doCropArgs.theme = api.settings.theme.stylesheet;
 		},
 
 		/**
Index: src/wp-includes/js/media-views.js
===================================================================
--- src/wp-includes/js/media-views.js	(revision 36536)
+++ src/wp-includes/js/media-views.js	(working copy)
@@ -283,7 +283,9 @@
 		content:     'crop',
 		router:      false,
 
-		canSkipCrop: false
+		canSkipCrop: false,
+		//Default doCrop ajax arguments, which allow other to extend it
+		doCropArgs: {},
 	},
 
 	activate: function() {
@@ -367,11 +369,14 @@
 	},
 
 	doCrop: function( attachment ) {
-		return wp.ajax.post( 'custom-header-crop', {
-			nonce: attachment.get('nonces').edit,
-			id: attachment.get('id'),
-			cropDetails: attachment.get('cropDetails')
-		} );
+		//clone the default args 
+		var data = _.clone( this.defaults.doCropArgs );
+		//Assign crop data
+		data.nonce = attachment.get('nonces').edit;
+		data.id = attachment.get('id');
+		data.cropDetails = attachment.get('cropDetails');
+
+		return wp.ajax.post( 'custom-header-crop', data );
 	}
 });