Gain permission from the owner of the funeral home. This may involve speaking to the manager, and asking him to give you contact details. Explain why you wish to film, and what you will be filming. Be completely honest, since you may need written permission.
Do not shoot any individuals, alive or dead, without their permission, or that of their loved ones. It is best to ask the employees of the funeral home to sign release forms, and to contact the families of the deceased to have them do the same. Be as sensitive as possible.
Inform the police that you will be filming within a funeral home. It is good practice to inform the police that you will be filming, wherever you are shooting. If they raise any objections to aspects of your filming, try to acquiesce to their wishes.
Be as quick as you can in filming the scene. Ensure that you are discrete. Funeral homes are sensitive areas, and you will have to respect the privacy of many of the mourners and staff.
Film during closed hours if you are shooting a work of non-fiction. This will allow you to avoid causing any consternation to employees or mourners. Shooting at night is the best option, since it is unlikely that you will disturb anyone.
Consider whether you need to shoot in a funeral home at all. Funeral home backgrounds can be replicated, and coffins can be built. You may be able to shoot the scene elsewhere, which will avoid any potential problems, and will make the process far easier.