Look at this js example:
var settings = {
"async": true,
"crossDomain": true,
"url": "http://./api/v1/topics/18/tags",
"method": "POST",
"headers": {
"authorization": "Bearer ",
"cache-control": "no-cache",
"content-type": "application/x-www-form-urlencoded"
},
"data": {
"tags[]": [
"closed",
"test"
]
}
}

$.ajax(settings).done(function (response) {
console.log(response);
});

2 things to consider:

1. content-type
2. tools to transform array to querystring - in my case jQuery will transform it to this - tags%5B%5D=closed&tags%5B%5D=test