State Nuclear Safety Participation Act of 1986 - Amends the Atomic Energy Act of 1954 to authorize the States to establish and enforce standards for the protection of the public health and safety from radiological hazards of production and utilization facilities. Requires that such safety standards be equal to or greater than Federal standards. Requires the Nuclear Regulatory Commission to notify States within ten miles of such a production or utilization facility that it intends to issue an operating license. Sets a 60-day deadline for such notification. Authorizes States to veto the issuance of licenses upon a written submission that the operation of such a facility would be contrary to the best interests of the State. Prohibits the Commission from issuing an operating license unless: (1) each affected State has certified to the Commission its approval and intention to implement emergency plans (including evacuation plans) approved by the Federal Emergency Management Agency (FEMA); (2) FEMA has notified the Commission in writing of such approval; and (3) the Commission finds that such plans adequately protect the public health and safety.