I am searching for a birth record from 1871, believed to be November. Did Monroe have any type of record system for this early of a date?

The problem I'm having is that I believe the child born was actually illigitmate and not entitled to the surname believed to be used. I also believe the child's father had died unexpectedly by the time of her birth. If there is any index, is it listed by date, or by surname? Where illigitimate births listed then, or were they able to be hidden?

I actually have the same problem with the same mother back in 1860 - Do I have any type of hope in finding this record?

Here's who I'm looking for:

Nov 1871 Birth - Addelaide (Addie); daughter of Sarah WHITMILL and (probably) Stephen SAGAR. Mother Sarah could be listed as a widow at this point. no doubt born in the Bedford area. Sarah may have been using the name of Lucy. I have sent to the state for the birth record under the name of Sagar, and it was not located

Approx. March, 1860 birth - Harriett. Mother probably Sarah Whitmill, aged 20. Father - ? Harriet is listing on the 1860 census. Sarah's mother had a child at approximately the same time, so I'm trying to determine who Harriett belonged to . She would never be referenced again.

I don't believe that either child was baptised near the time of their birth.

All help appreciated!!