B737 flight crew reported possible malfunction with aircraft brakes during taxi to runway. Requested tow back to gate.

Narrative

After leaving the CDF (Central Deice Facility) and being told to expect XXL they changed runways on us and wanted us to taxi to XYR. The instructions they gave us were to taxi on [Taxiway] 1 and hold short 2. As we were taxiing down 1 to hold short of 2 Captain mentioned he was having trouble stopping aircraft and let Ground know we would go past 2 due to poor braking as the taxiway in this area looked fairly bad. Once passing 2 taxiway looked much cleaner and we were told to keep taxiing on 1 to 3 and do a U turn to join 3 and 4 to taxi towards XYR. As we are taxiing at minimal speed Captain mentions he has brakes fully pressed in trying to stop but nothing is happening and we had no skidding/sliding going on. At this point I joined the Captain on the brakes and press them fully in with no stop either. Aircraft came to a stop about 10 seconds in total after. Other aircraft infront of us did not report issue with taxiway and ATIS did not state poor conditions on taxiway. At this point we were afraid to keep going as we did not know if we had a brake issue and we were going to ZZZ1 which is short runway. We also did not know if deicing fluid got in the brakes. We felt the safe decision was to return to gate with a tow as we did not want to not be able to not stop and go off the taxiway or hit something. Wrote plane up at gate. Cause: Taxiways were not reported to have poor conditions. Aircraft infront of us did not report poor braking or issues. We felt we had a brake issue going on and did not want to risk going off the taxiway or hitting something so we made the safe call to stop and get a tow to gate.