A blue screen indicates that there was a hardware issue that caused that hardware to stop, therefore shut windows down. It may not be the hard drive it could be the CPU, the integrated graphics, a memory stick (RAM), a peripheral card like an additional sound or video card, or the motherboard it self causing the issue. It could be anything unless it's specifically saying it was the hard drive that stopped and if a hard drive stopped and caused a blue screen it's the drive windows is installed on. Hard drives don't run until and unless you call upon them by opening them or a file on them so a hard drive that isn't the one windows is installed on will not cause a blue screen. The only way a hard drive that is not the primary windows drive can do that is if you're running a game or program or something that's on that drive and it stops.
Running check disk is a good thing to do to investigate the problem. Check Disk is a windows utility, it's there. You just have to run it.
In windows 8 and 10 right-click on the Drive in File Explorer that you want to check and select Properties. Then click on the Tools tab at the top of that window. In the Error Checking section click on the Check button. This option will check the drive for file system errors. If the system detects that there are errors, you will be asked to check the disk and windows will attempt repairing it. You also have the option to run CheckDisk the next time you restart or boot it up. This is a good idea to do because it will do a more thorough and lower level scan because it performs the scan before windows starts - nothing on the drive is being used so it scans more of the drive than it will while windows is running.