A vim-fugitive status window toggle (mapped to F3). Seems to work nicely

ToggleGStatus

function! ToggleGStatus()
    if buflisted(bufname('.git/index'))
        bd .git/index
    else
        Gstatus
    endif
endfunction
command ToggleGStatus :call ToggleGStatus()
nmap <F3> :ToggleGStatus<CR>

@kenichi bufname accepts a file pattern, you could use

bufname('fugitive:///*/.git/')

to match the fugitive Git buffer
and then you can use

 execute ":bdelete" bufname('fugitive:///*/.git/') 

to delete the buffer
EDIT:
Fugitive adds a second / at the end, use

bufname('fugitive:///*/.git//$')

For thos who wants this in lua for neovim

local function showFugitiveGit()
  if vim.fn.FugitiveHead() ~= '' then
    vim.cmd [[
    Git
    " wincmd H  " Open Git window in vertical split
    " setlocal winfixwidth
    " vertical resize 31
    " setlocal winfixwidth
    setlocal nonumber
    setlocal norelativenumber
    ]]
  end
end
local function toggleFugitiveGit()
  if vim.fn.buflisted(vim.fn.bufname('fugitive:///*/.git//$')) ~= 0 then
    vim.cmd[[ execute ":bdelete" bufname('fugitive:///*/.git//$') ]]
  else
    showFugitiveGit()
  end
end
vim.keymap.set('n', '<F3>', toggleFugitiveGit, opts)

EDIT: fixed typo

@Fymyte thank you very much!

side note - experimenting both with and without the '$'; while i appreciate that it mimics the original behavior closer with it, i actually kind of like it without.

@Fymyte Thanks for the lua snippet! (p.s. there is a typo, it should be if vim.fn.buflisted(vim.fn.bufname('fugitive:///*/.git//$')) ~= 0 then)

@disselkamp thanks for the report 👍