Sowing seeds of shemitah produce

Answer

It is forbidden to plant foods with kedushat shevi'it (indoors, or after the shemitah year ends). It is only permissible to eat or benefit from them in a similar manner of eating (drinking, anointing [oil], lamp oil, painting – see Rambam, Hilchot Shemitah 5:1). However even if the fruit or vegetable has kedushat shevi'it, this does not necessarily mean that its seeds or pits do, too. There are three levels:

1. Seeds that are completely inedible do not have kedushat shevi'it, so it is permissible to plant them (apricot seeds, for example).
2. Seeds are not eaten by themselves, but are sometimes eaten as part of the fruit/vegetable: most opinions hold that they do not have kedushat shevi'it. For this reason, they can be planted (Cucumbers and grapes, for example).
3. Seeds that are eaten on their own, such as watermelon and pumpkin seeds, they have kedushat shevi'it so they may not be planted.