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Does it need to be on me whenever I am flying?
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Yes.
Whenever you are flying, you need to have your certificate and your medical on you.
§ 61.3 Requirement for certificates, ratings, and authorizations.
(a) Pilot certificate. A person may not act as pilot in command or in any other capacity as a required pilot flight crewmember of a civil aircraft of U.S. registry, unless that person --
(1) Has a valid pilot certificate or special purpose pilot authorization issued under this part in that person's physical possession or readily accessible in the aircraft when exercising the privileges of that pilot certificate or authorization. However, when the aircraft is operated within a foreign country, a current pilot license issued by the country in which the aircraft is operated may be used; and
(2) Has a photo identification that is in that person's physical possession or readily accessible in the aircraft when exercising the privileges of that pilot certificate or authorization. The photo identification must be a:
(i) Valid driver's license issued by a State, the District of Columbia, or territory or possession of the United States;
(ii) Government identification card issued by the Federal government, a State, the District of Columbia, or a territory or possession of the United States;
(iii) U.S. Armed Forces' identification card;
(iv) Official passport;
(v) Credential that authorizes unescorted access to a security identification display area at an airport regulated under 49 CFR part 1542; or
(vi) Other form of identification that the Administrator finds acceptable.
(b) Required pilot certificate for operating a foreign-registered aircraft. A person may not act as pilot in command or in any other capacity as a required pilot flight crewmember of a civil aircraft of foreign registry within the United States, unless that person's pilot certificate:
(1) Is valid and in that person's physical possession, or readily accessible in the aircraft when exercising the privileges of that pilot certificate; and
(2) Has been issued under this part, or has been issued or validated by the country in which the aircraft is registered.
(c) Medical certificate. (1) Except as provided for in paragraph (c)(2) of this section, a person may not act as pilot in command or in any other capacity as a required pilot flight crewmember of an aircraft, under a certificate issued to that person under this part, unless that person has a current and appropriate medical certificate that has been issued under part 67 of this chapter, or other documentation acceptable to the Administrator, which is in that person's physical possession or readily accessible in the aircraft.