Question
Can sod (centipede) be placed on top of winter rye grass without tilling the soil?

Answer
Yes. However you should first apply an organic product like "Milorganite" to aid root development of the new sod. Then mow the existing vegetation with your lawn mower set at the lowest height. You really want to scalp the existing lawn. Put down the sod and jam it in well; roll it if possible and then start a good watering program.
If it is too hard to scalp the lawn with your mower, it is well worth it to pay a commercial operator a one-time fee to scalp it for you. Commercial operators have machines that are powerful enough to do this kind of work.