I'm reading through the Ohio Replevin laws, and that's just how it works.
And I'm not a lawyer, this is just how I'm interpreting it.
Remember, Movant = Veronica, Respondent= Penny/COSR
http://codes.ohio.gov/orc/2737
Veronica and her attorney filed a Motion and affidavit for order of possession of property. This is a document that describes the property (Piper) and the approximate value, the specific interest of the movant in this property (why she wants Piper back), How Penny/COSR came into possession of Piper, How Penny/COSR has used the property (I have no idea?), the extent of any damages, if any (such as if Piper were to be spayed or harmed), best knowledge of the location of Piper, and that the property wasn't taken for other legal reasons that don't apply in this case. The order of possession doesn't become effective until a bond is filed for twice the approximate value, or cash is deposited with the court for twice the approximate value. This is the $10,000 Veronica paid.
Then they sent the respondent (Penny/COSR) a notice of motion for an order of possession. After that, the respondent has 5 business days to deliver a written request for a hearing or file a bond matching the amount of the Movant ($10,000 in this case).