Texas son looking for mother born in MI

After many, many years things in my life have now led me to search for my birth mother. More than anything I want her to know that I'm OK and turned out fine.:) Through my search I have learned that I have at least 1 sibling and possibly a sad story involving her. I must say the details are still unclear but I do know this was a last minute "adoption at birth". I also know at 21 years old she came to Dallas, Texas and stayed briefly at a "rented apartment" to give birth to me on Christmas eve 1965. I can only imagine how heartbreaking of an experience it was for her... Over the last two weeks I have done a tremendous amount of research both on the INTERNET and with in person interviews. I have reached a stopping point as I need to search within the Michigan birth records and cannot find access. If anyone can help or advise me it would be greatly appreciated. Information listed on my previously sealed birth certificate is: Adoptee DOB 12-28-1965 Gender - Male Name - Baby Boy Smith Place - Methodist Hospital, Dallas Texas Birth Certificate Number 142-65-212446 Cause Number - A-5458-JUV Birth Mother Name - Karen Elizabeth Smith Age at Birth - 21 Marriage status - Single Other children at birth - 1 Birthplace - Michigan Other information This was a last minute private adoption before birth. The birth mother moved into a "Rented Apartment" on 810 N. Lancaster Rd, in Dallas Texas. This was walking distance to the doctors office and the hospital. I have spoken to the attorney (Joe Brown Jr.) and the delivering doctor Robert Moore. I viewed my parents adoption file from the attorney but he has no file on the mother. There is evidence that he was contacted just days before the birth as well. One last piece of information is the signature of the court document for Karen Elizabeth Smith looks perfect. I believe it was not an alias as it looked very fluid. All the address information below that signature was left incomplete. Can anyone help me find information relating to a Karen Elizabeth Smith born in Michigan 1944 or 1945?