The Channel 4 drama will be directed by Toby Haynes.
The actor has spoken of running his own production company, too.
Netfilx has posted a behind-the-scenes video on social media.
The comedian known as “America’s Dad” was convicted of drugging and molesting a woman – one of dozens of accusers.
She said David Tennant was her favourite Doctor.
The six-part series will be shown on BBC One later this year.
The BBC show will continue to trick and terrify viewers.
The former singer has also aired her views about feminism on social media.
The fashion designer was shot dead by serial killer Andrew Cunanan in 1997.
The claims include an allegation being investigated by British police.