Date: 201911
Local time of day: 1801-2400
Location: ZZZ.ARTCC, US
Weather elements / visibility: Turbulence
Aircraft: EMB ERJ 190/195 ER/LR
Operator: Air Carrier
Operating under: Part 121
Mission: Passenger
Flight phase: Cruise
Airspace: Class A ZZZ
ATC / advisory: Center ZZZ
Reporter organization: Air Carrier
Reporter function: Pilot Not Flying; First Officer
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Human factors: Confusion; Other / Unknown
Second reporter function: Pilot Flying; Captain
Anomaly: ATC Issue All Types; Flight Deck / Cabin / Aircraft Event Other / Unknown
When detected: In-flight
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: Shortly after leveling off at our cruising altitude Captain; who was PF (Pilot Flying); assumed control of the radios while I; PM (Pilot Monitoring); took a few minutes to eat a crew meal. During this short period Captain queried ATC asking for an altitude change to a lower; and hopefully smoother; altitude. After his request; an ATC supervisor keyed in asked him if 'everything was okay' and it 'sounds like you're slurring your words'. Captain said everything was fine and that we were just getting bounced around due to the ride conditions. I finished my meal; returned to working the radio; and we landed uneventfully. Due to an aircraft swap; we had to exit security to transition to another terminal. Once outside security; Captain made several calls to the ZZZ Chief Pilots; Duty Pilot; and [Company] for guidance on how to handle the situation. We didn't want to show up to our next aircraft with ATC thinking we weren't fit to fly. With helpful information from all available resources it was determined that two managers would meet us to assess Captain fitness for duty through a series of questions. The questions were administered and we were cleared to board the aircraft and work our last leg of the night back to ZZZ1.Captain's voice; slight accent; and the ride conditions attributed to ATC's questioning. While I do not know what Controllers are trained to listen for specifically; I understand that if they were concerned about our well-being that they would ask the questions they did. Simply; Captain could annunciate more and be clearer when using the radio. ATC could have explained what they were asking about in a little more detail.


Second narrative: Center made a comment on the radio when we were at FL230 and I requested FL210 due to moderate turbulence. Since the FO (First officer) was eating his crew meal at cruise; I clicked the mike and asked for lower. The ATC Supervisor got on the radio questioning if everything was alright alleging slurred speech. I did not acknowledge her comment in an open frequency; other than restating the reason for our request for altitude change. Since the comment was made on a non-discreet frequency; I did not want to allow the comment to snowball into an unnecessary issue while in flight.As soon as we landed and deplaned; my first phone call was to Chief Pilot since I had both of their cell phone numbers saved on my phone. Since I got no response back from either Chief Pilot; I contacted the [Company] safety hotline. I immediately received a call from a [Supervisor]. [Supervisor] advised me not to proceed to gate and to immediately call the Duty Chief. She told me that she would call me back. I received a call back; and she told me that two managers were going to meet us to conduct an impairment evaluation at the gate.I also received a call from ZZZ Chief Pilot. He told me to wait for the two managers and that he would call me back with a decision of whether we could continue to our next flight or not.The two managers showed up at the gate; and I suggested for us to step into an unused; empty jetway to conduct the process away from passengers and other employees. They agreed. They interviewed the FO and me and they asked a number of pertinent questions that were on what it seemed to be an official [Company] form. They filled out the form according to our answers. After we answered all of their questions; I told the FO that we would remain away from the gate area until I received the call from Chief Pilot. Chief Pilot called me back and gave us the 'OK' to continue flying.We boarded the flight and; after performing all preflight duties; we pushed. The next morning; I received a call from Chief Pilot and I briefed him on what had happened the night before. I later received a call from Chief Pilot.


Synopsis: EMB-190 flight crew reported ATC Controller suspected slurred speech by Captain.