There's actually no evidence that Rasputin ever touched the Tsarina. If he had, the Tsar would not have protected him from the husbands of all the noblewomen he did fuck.

Which was actually a large part of why Rasputin was murdered.

He was a consummate con-man, and practiced "sexual healing", but the Tsar and Tsarina protected him because he kept "healing" their son, who was a hemophiliac and Rasputin's "healing" was mostly keeping the quack doctors from killing the kid with mercury and blood-letting.

Rasputin was also a commoner, and tried to get Nickolas to stop killing his own people so much... That one didn't really take.

Another fun fact, the noblemen (read, angry husbands) who murdered Rasputin played up the event, claiming to have to kill him half a dozen times, so that the Tsar would believe that Rasputin was some sort of demon. Which would then get the Tsar to not murder them for killing the guy who was keeping his son alive.