Firstly, we know that Paris is a gentleman and of noble blood. There are a number of references in the play which confirm this.'

"there
is a nobleman in town, one Paris,"

Nurse when speaking to Romeo in Act 2, scene 4

"Sir Paris, I will make a desperate tender
Of my child's love"

Lord Capulet addressing Paris in Act 3 scene 4.

"The gallant, young and noble gentleman,
The County Paris ..."

Lady Capulet's reference when speaking to Juliet in Act 3, scene 5.

Lady Capulet also refers to Paris as "county" which means that he is a count.

Prince Escalus, Prince of Verona, mentions at the end of the play that:

"And I for winking at your discords too
Have lost a brace of kinsmen"

The prince is here referring to the fact that he has lost two kinsmen as a result of the ongoing dispute between the houses of Capulet and Montague. Earlier in the play, after Mercutio and Tybalt had been killed, he also said:

"I have an interest in your hate's proceeding,
My blood for your rude brawls doth lie a-bleeding"

In this instance, he was referring to Mercutio's death.

The two kinsmen that Prince Escalus has lost are therefore Mercutio and Paris. Paris is thus a blood relative of both Prince Escalus, Prince of Verona, and Mercutio.

In Romeo and Juliet, to whom (or to what family) is Count Paris related?

Count Paris or also referred to as County Paris, is a suitor of Juliet.  He is related to Prince Escalus, the Prince of Verona.  He is described as handsome and wealthy.  

Count Paris is kinsman to Prince Escalus.

Count Paris is a kinsman to Prince Escalus.

There are three family circles in Romeo and Juliet. The family of Prince Escalus is the third family in the play. This family includes the Prince, Count Paris, and Mercutio (Romeo's best friend. This family truly acts as the peacemakers as Mercutio is Romeo's best friend and Count Paris is to marry Juliet.

Paris is related to Prince Escalus (the ruler of Verona).