First you'll need to grab the user's orders. Then you can check the product type through the purchasable.
Something like this:
{% set orders = craft.commerce.orders.user(currentUser).find() %}
{% if orders|length %}
{% for order in orders %}
{% for lineItem in order.lineItems %}
{{ lineItem.purchasable.product.typeId }} {# 1 #}
{% endfor %}
{% endfor %}
{% endif %}
You can take that a step further by doing something like this:
{% set orders = craft.commerce.orders.user(currentUser).find() %}
{% set product = false %} {# set the condition to false by default. #}
{% if orders|length %}
{% for order in orders %}
{% for lineItem in order.lineItems if lineItem.purchasable.product.typeId == 1 %}
{% set product = true %}
{% endfor %}
{% endfor %}
{% else %}
{# No orders found. #}
{% endif %}
...
{% if product %}
{# User has purchased product type at some point in time. #}
{% else %}
{# User has never purchased product type. #}
{% endif %}