Permission needed
1. What the city publishes
Is metal detecting allowed in the parks? Yes. A permit may be obtained for free at the Idlewild Park Office, 2055 Idlewild Dr.
2. The state rule also applies
The park supervisor can authorise the device, NAC 407.103, and that covers only land the state parks division runs. Removing a historical relic from that land is separately prohibited by NRS 407.250(2), which no supervisor waiver touches. NRS 383.435 reaches further: "state land" is defined by NRS 383.425 as land owned or controlled by a state agency or political subdivision, so removing or excavating a historic or prehistoric site on county or city land is a gross misdemeanour at first offence. Discovering a native Indian cairn or grave carries an immediate duty to report on any land, NRS 383.170, a $500 fine to fail.
Nevada state law also reaches city land. The state page sets out how.
3. County rules
Awaiting review.