I had a look at the Broome council regs and acts, and like many councils, there are no specific rules/regs relating to detecting local parks. Though interpretations from other existing acts such as damaging flora on local government property may be enforced if seen to be detecting in an inappropriate area, or if causing damage. In such cases, if directed by council workers to leave, best to do so. If you are not confident on recovering deeper items without digging huge holes or plugs, stick to surface or near surface finds.
Just take care on where you detect with regards to recovering items around sensitive areas. Playing fields are no go, and pristine turf is better left as is unless you have perfected unobtrusive recovery methods that will not cause damage or leave a mess. Take great care where underground irrigation might be present, use a cloth to catch any loose dirt from your recovery, and properly dispose of any junk found.
Also never take a shovel into parks, especially due to the chance of cutting through irrigation lines, plus it will definitely be frowned upon by onlookers. Use a screw driver to locate and flick coins out of the ground, or have a look a the "slit" revery method using hand tools mentioned in the finds section.
Lastly, if you don't already own an electronic pinpointer to aid in recovery, I'd strongly advise you to purchase one . It will save you a lot of time, and will minimise any damage caused during recovery.
