Narrative:

Departing runway zzc at ZZZ; we were given takeoff clearance as follows; 'aircraft X; fly runway heading; clear for takeoff runway zz center.' in my mind; this clearance means to disregard the standard [departure] procedure of making the left turn to heading 330; and instead maintain runway heading until further advised. We maintained runway heading; then the tower controller asked us if we were going to make the turn to 330; which we immediately did when prompted. We were transferred to ZZZ departure; and upon checking in were informed that we needed to call a number due to possible pilot deviation. The flight proceeded as normal from that point on. Upon making contact with ATC via the provided number; the captain was informed that it was a non-issue; and that the event did not cause an unsafe situation.the tower controller was particularly busy; with long lines of both zzc departures as well as zzl arrivals waiting to cross the runway into the ramp. I believe that it's possible that for this reason the tower controller either issued the fly runway heading instruction in error; or simply forgot that he had done so; leading to the assumption that we had deviated by not flying the published 330 heading.be extra cautious especially when ATC seems to be busy and approaching task saturation; as they are liable to make mistakes just like anyone else. Also; when it's the first officer's (first officer's) leg; sometimes the transfer of control/radio responsibilities entering the runway can make things seem a bit rushed. Ensure that the takeoff clearance is fully understood and read back word for word.

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Original NASA ASRS Text

Title: CRJ-900 First Officer reported that they departed flying runway heading when they should have flown standard departure heading.

Narrative: Departing Runway ZZC at ZZZ; we were given takeoff clearance as follows; 'Aircraft X; fly runway heading; clear for takeoff Runway ZZ center.' In my mind; this clearance means to disregard the standard [departure] procedure of making the left turn to heading 330; and instead maintain runway heading until further advised. We maintained runway heading; then the tower controller asked us if we were going to make the turn to 330; which we immediately did when prompted. We were transferred to ZZZ departure; and upon checking in were informed that we needed to call a number due to possible pilot deviation. The flight proceeded as normal from that point on. Upon making contact with ATC via the provided number; the captain was informed that it was a non-issue; and that the event did not cause an unsafe situation.The tower controller was particularly busy; with long lines of both ZZC departures as well as ZZL arrivals waiting to cross the runway into the ramp. I believe that it's possible that for this reason the tower controller either issued the fly runway heading instruction in error; or simply forgot that he had done so; leading to the assumption that we had deviated by not flying the published 330 heading.Be extra cautious especially when ATC seems to be busy and approaching task saturation; as they are liable to make mistakes just like anyone else. Also; when it's the FO's (First Officer's) leg; sometimes the transfer of control/radio responsibilities entering the runway can make things seem a bit rushed. Ensure that the takeoff clearance is fully understood and read back word for word.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.