F#: Disposing of resources that are inside a closure?

Suppose I create a closure over a resource such as a StreamWriter:

let currentdir = Directory.GetCurrentDirectory()
let testfile = sprintf "%s\\%s" currentdir "closuretest.txt"

let getwriter() =
    let writer = new StreamWriter(testfile, false)
    (fun() -> writer.Write "test")

Is there a way to close the StreamWriter when I'm done with the closure? Or do I need to replace the closure with a wrapper object that has a Write() method and a Dispose() method? (This is of course a trivialized example.) Thanks all.