I am using a external crystal as a clock source. the clock freq is 27MHz.
Using a scope and probing x1 and x2 input pins(crystal). The signal across the
crystal are very different. One is sinusoidal while the other is distorted.
You don't say what the chip is, but it sounds normal. The crystal is not a "clock source" - it is the resonant component in an oscillator. The oscillator if formed with the two chip pins. One pin will be an input, the other will be the output. The signals will be very different.
The XIN signal would always be near to a sine, the XOUT may be different depending on the clock oscillator design. A "simple" clock oscillator is CMOS inverter with excess gain, that drives the crystal with a more or less rectangular waveform at XOUT. A modern EMC optimized oscillator uses a lower drive level. XOUT looks more like a sine in this case.