Is the "imported graphic" embedded or linked?
I will leave this one for james to finished since he started it but just in case you have to embed the image if you want to color it in Illustrator, it has to be a grayscale tiff, if it is not then you can go to Edit>Edit Colors>Convert to Grayscale then make sure it is selected and then simply chose a fill color.
Oh, version 12.0.1
Go to online Help and search for Colorize.
The ability to "colorize" grayscale and 1-bit raster images is not listed in the new features section of CS3's online Help, so I assume it was probably bragged about as if it were something new invented by Adobe in CS2. This ability amounts to nothing more than sending 1-bit or grayscale data to user-specified separation plate(s), and is one of many basic features that other programs were doing for about 15 years before Illustrator finally caught up.
The image does NOT have to be TIFF format (1-bit and grayscale JPEG, 1-Bit BMP also work), and it does not have to be embedded.
There are other ways to "colorize" raster images, regardless of their color depth:
You can store an embedded image as a Symbol, and use the Symbol Stainer to tint the Instances.
You can use an image (any color depth, linked or embedded) as an Opacity Mask for a path filled with the desired color.