Necessary to save used registers in assembly ?

I am using assembly language routines
called from C code.
Within the assembly routines, is it necessary to save the registers used?

Ex:
MY_ASM_ROUTINE:
PUSH ACC ; necessary ?
CLR A ; overwrite ACC
POP ACC
RET

main(){
MY_ASM_ROUTINE();
}

Or does the C compiler assume that
registers can be overwritten by
calls to routines?

I couldn't find the answer in the manuals.

Thanks in advance
Jim Burke