You can shoot and kill cranes and other migatory birds such as herons
if they are destroying property. Here's how:

Call USDA Wildlife Services at 303-236-8171 and explain to them that
you are filing a migatory bird depredation permit application and need
form 37. Explain to them that a crane (or whatever bird) is destroying
your property and you would like to destroy it.

Once you get form 37 go to http://forms.fws.gov/3-200-13.pdf , fill it
out and send it in. Once you get your permit you'll be able to destroy
the bird legally.

Sam