I think you would want to check if your wrapping p element is visible, using $("p").is(":visible").
If it is visible, pause the video using document.getElementById("yourVideoId").pause(), obviously replacing "yourVideoId" with whatever you have in the id attribute on your <video> tag. Then, after you do that, you can call .toggle() on your p element.
If it is not visible, and the user clicks your toggle button, I would imagine you would just want to show the video, and not resume playing it, as that might be a little jarring to the user. If you do want that functionality, however, just add document.getElementById("video").play() in the else block in the example below.
Here is a working example to demonstrate the functionality:
$(document).ready(function() {
$("button").click(function() {
var p = $("p");
if (p.is(":visible")) {
document.getElementById("video").pause();
$(this).text("Show");
} else {
$(this).text("Hide");
}
p.toggle();
});
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<p>
<video id="video" controls width="40%">
<source src=http://techslides.com/demos/sample-videos/small.webm type=video/webm>
<source src=http://techslides.com/demos/sample-videos/small.ogv type=video/ogg>
<source src=http://techslides.com/demos/sample-videos/small.mp4 type=video/mp4>
<source src=http://techslides.com/demos/sample-videos/small.3gp type=video/3gp>
</video>
</p>
<button>Hide</button>
Added width="40%" on the video so it fits in the snippet window.