Marshall County public records are available as certified copies to eligible people, and will be issued once you fill out the request form and pay the current search fee. For most vital records, it's $15 each and you can get multiple copies of the same record for $6 apiece.
You an send a mailed application but you will get faster results if you go to the health department office in Guntersville instead. They are open to the public Monday to Friday during standard business hours, and you can just go to the counter with your paperwork and make your request. Forms are available at the counter or you can download them before you go from the Alabama Department of Public Health website. Just search for "vital records".
If you are going to mail your application, you have to include the proper fees as either a check or money order. It should be made out to the State Board of Health. Normally you would show ID at the counter, so you need to include a clear photocopy of your photo ID (drivers license, etc) with your application package. You can mail the whole thing to the Guntersville health department, or even to the main Vital Records office in Montgomery. Mailed requests generally take about 7 to 10 days for a response back.
Marshall County Birth Records
Everyone is permitted to get a copy of their own Marshall County birth record, as well as copies for their own children, parents, siblings or current legal spouse. These are issued without restriction. But if you are looking for records for someone outside your immediate family, they are not going to be released until 125 year have passed after the date of birth due to state privacy laws. Records of that age are also freely accessible through the State Archives.
Marshall County Death Records
The same privacy restrictions are in place for Marshall County death records except that the period is only 25 years before they are made public. After 25 years, they are also available through most libraries, State Archives and even online through several large genealogy websites that post databases of public domain records. But if you need a certified copy for legal reasons, you'll need to go to the health department.
Marshall County Marriage Records
Marshall County marriage records are the simplest to find because there are no privacy laws pertaining to them. You can just make a request and get a copy of any record you want, regardless of how old it is and how you are related to the parties on the certificate. State records start in 1936 for marriage registrations, and in 1950 for divorces.
Marshall County Criminal Records
This records are different from the above listed vital records, and they are kept strictly confidential. They are also maintained by the state rather than the county, so even Marshall County criminal records can only be retrieved from the Alabama Criminal Justice Information Center in Montgomery. They can be requested by mail, but only if you are ordering your own records. The cost per search is $25, and their website has blank forms for you to print out.