Compared to some other Massachusetts counties, Norfolk is one of the newer ones. It was officially established in 1793, from territory that was originally part of Suffolk County.
When searching for Norfolk County public records, you will have relatively easy access though not all records are housed in one location. You will have to direct your request to the right office, depending on what era your desired records are from.
The oldest records will date to at least 1793, but likely farther back if you look for Suffolk County material. For these records, up until 1841, you have to do your research at the county clerk's office in Dedham. You can make a request there in person, or by mail. The proper forms to request any Norfolk County public records can be printed out at home from the Office of Health and Human Services website for Massachusetts.
In 1841, the state made it mandatory that the counties submitted these vital record registrations. So records after that date (but before 1921) are housed in the State Archives in Boston. You are free to do all the research you wish at the location, without having to actually put in applications for each record you need.
And then after 1921, these are considered more "active" records, and they are kept by the Registry of Vital Records and Statistics (a state office). Applications can be made by mail, using the same forms as mentioned above for the county clerk's offices. There is only one form for all 3 kinds of vital records.
Norfolk County Birth Records
Vital records in Massachusetts are considered public domain, so you can order any Norfolk County birth record that you want regardless of whether you are even related to that person. The cost for each record is $28 when you send a mailed application, or $18 if you visit an office service counter. At the counter, you will get your records while you wait but a mailed in form can take up to a month to be processed.
Norfolk County Death Records
There are no restrictions on Norfolk County death records, and the fees will apply for either mailed-in or in-person applications ($28 or $18 respectively).
Norfolk County Marriage Records
The same goes for Norfolk County marriage records. The fees are the same, and they are publicly available from the same outlets as the other types of vital records.
Norfolk County Criminal Records
You won't be able to order Norfolk County criminal records in the same way as any of the others. These are not kept by the county, and you have to send any requests by mail to the Department of Criminal Justice Information Services (DCJIS). These files will cost $30, and you are legally allowed to request your own files, as well as any other criminal records that have been made public. That will be determined by the crime involved, the sentence and what the current parole status is for the person. The DCJIS website has all the details.