One party of phone conversation recording that phone conversation without the permission of the other party is a crime under Nevada law, but is not a crime under Federal Law. Although most other states follow the Federal law, Nevada is stricter, probably due to a history in the State of protecting individual rights and privacy.
Under federal law a party to a phone call may wiretap it without anyone else's permission. However if the person doing the wiretapping is not a party to the phone call, then he/she would need to get either a search warrant or every party's permission in order to wiretap the call legally. 18 U.S.C. § 2511(2)(d) (1970) ("It shall not be unlawful under this chapter for a person not acting under color of law to intercept a wire, oral, or electronic communication where such person is a party to the communication or where one of the parties to the communication has given prior consent to such interception unless the communication is intercepted for the purpose of committing any criminal or tortious act in violation of the Constitution or laws of the United States or of any State.").
Under Nevada law, Nevada is an "all-party consent" state because every party to a phone conversation needs to give permission in order for the call to be wiretapped legally. Nev. Rev. Stat. Ann. §200.620; Lane v. Allstate, 969 P. 2d 938, 941 (Nev. 1988). However, when the conversation is "in person" rather than over a wire, then only one party to the conversation needs to consent to the recording. Nev. Rev. State. Ann. §200.650.