Fire Station Construction Grants Act This bill directs the Federal Emergency Management Agency (FEMA) to establish a grant program to modify, upgrade, and construct fire and emergency medical services (EMS) department facilities. Grant recipients may use funds to build, rebuild, or renovate fire and EMS department facilities; upgrade existing facilities to install exhaust emission control systems, install backup power systems, upgrade or replace environmental control systems (such as HVAC systems), remove or remediate mold, and construct or modify living quarters for use by male and female personnel; and upgrade fire and EMS stations or build new stations. Grant recipients must meet one of the two most recently published editions of relevant codes and standards, especially codes and standards that (1) require up-to-date hazard resistant and safety provisions, and (2) are relevant for protecting firefighter health and safety. The bill sets forth provisions regarding (1) grant fund allocations between career and volunteer fire and EMS departments, (2) overtime, and (3) prevailing rate of wage and a requirement for using materials produced domestically for public contracts.