CRTs don't, as a rule, emit sound (other than the one-time "hiss of death"). If the sound is coming from the speaker, it's probably a leaky capacitor somewhere in the audio circuit. Another common source of high-pitched sounds is the switching power supply. Loose magnetic components (e.g., transformer coils) can vibrate.
If it really sounds as if it's coming from the CRT, it may be the deflection yoke. The horizontal deflection frequency is probably too high to be audible, but a harmonic of the vertical deflection frequency would be well within the audible range. If one such harmonic happens to coincide with the mechanical resonant frequency of some loose thing, it could squeal.