Is there a recovery period after amniocentesis?

Yes. Minimal. Women walk out of the office after an amnio. From the mother's point of view the recovery is no different from having gotten an immunization - a little soreness at the needle site. Women should rest a bit if they are feeling contractions after the amnio, which is not uncommon for a short period of time.
Usually not. Most physicians allow their patients to resume their normal activities after an amniocentesis. Some physicians do recommend bed rest for a period of time after an amnio, but the studies show that complication rates are the same and the risk for problems is very, very low after an amnio.