As of Python 3.9, json.tool has a new --no-ensure-ascii option for this.
Before 3.9, you'll need to use something else. This is (most of) the source for the 3.8 version of json.tool:
prog = 'python -m json.tool'
description = ('A simple command line interface for json module '
               'to validate and pretty-print JSON objects.')
parser = argparse.ArgumentParser(prog=prog, description=description)
parser.add_argument('infile', nargs='?',
                    type=argparse.FileType(encoding="utf-8"),
                    help='a JSON file to be validated or pretty-printed',
                    default=sys.stdin)
parser.add_argument('outfile', nargs='?',
                    type=argparse.FileType('w', encoding="utf-8"),
                    help='write the output of infile to outfile',
                    default=sys.stdout)
parser.add_argument('--sort-keys', action='store_true', default=False,
                    help='sort the output of dictionaries alphabetically by key')
parser.add_argument('--json-lines', action='store_true', default=False,
                    help='parse input using the jsonlines format')
options = parser.parse_args()
infile = options.infile
outfile = options.outfile
sort_keys = options.sort_keys
json_lines = options.json_lines
with infile, outfile:
    try:
        if json_lines:
            objs = (json.loads(line) for line in infile)
        else:
            objs = (json.load(infile), )
        for obj in objs:
            json.dump(obj, outfile, sort_keys=sort_keys, indent=4)
            outfile.write('\n')
    except ValueError as e:
        raise SystemExit(e)
The problem is you have no way to add parameters to the call to json.dump - you'd want to do this instead:
json.dump(obj, outfile, sort_keys=sort_keys, indent=4, ensure_ascii=False)
But you'll have to write your own script for that, json.tool won't help you here.